Should I leave playing chess or not based On this experience

No.
Did both of you record moves on score sheets?
Score sheets provide evidence to resolve all such disputes.

I would just fart before mating and wait for your clock to run down to 10 seconds before mating. Let them get a whiff of your superiority.

BTW please 😌 don't leave chess.

Don't quit chesscom. Quit that arbiters tournaments
But he doesn't need to!
Its nice to see someone who is principled in this community for once. I have personally resolved to play with a small group of people when I'm not playing bots. There are too many people on this site who have forgotten that this game has two sides to it and they have forgotten their sportsmanship with it. I wouldn't give up on such a wonderful game. I would just give up on the people playing it.

If you leave, will you feel better about life? Imagine not playing, and how that would feel to you. If you think it would create less stress and better mental health, I say leave because you can always go back. Maybe you just need a break.

If you leave, the bad one win. Just remember, during a tournament you should be writing down each move, as should your opponent, unless it's a bullet tournament of course. So if it were to happen again, just present the record of the moves, and show how it doesn't lead to the position currently on the board.
But, being correct isn't the only thing. The arbitrator, remember, doesn't know you are correct. All they know is that there is an issue to resolve. If you talk over them, you will give them the impression that you are the one mistaken. Always remember, if you are in the right, then there is no rush. If your opponent gets to speak first, then just let your opponent speal off their side, and then, when they are finished, calmly and clearly present your concern, show your record of the moves played, and do not interrupt or talk over the arbitrator (don't make their job harder - they aren't against you if they ask your opponent a question - they are doing their job by questioning both sides). Of course, your opponent may interrupt you, and if so then don't "fight back" but rather stop talking and just look at the arbitrator so they can admonish them - you stay out of casting judgement on your opponent's behaviour because all you want to do is present the issue regarding the moves played, and the current position on the board. Remember, you just want the move issue resolved, and in the end, solving the personality problems of your opponents is way out the pay bracket of the tournament arbitrators and also not really yours to solve either!
In any activity you do in life that you enjoy, there will be times when you find that some of the people who share your interests are just plain jerks. That's life, you can't prevent it anymore than you can prevent your opponent from choosing a defence you dislike in response to your favourite opening. In the end, you just learn how to deal with it, and make the best choices you can. Just don't get down into the mud to wrestle with a pig, as you both get dirty, but only the pig likes it.
- Jeff

What can I do in that time because that tournament didn’t have the convenience of letting players write their moves over the score sheet. And *BTW I AM COVEYING A BIG GRATITUDE TO ALL THOSE WHO HAVE GIVEN ME THE WILL TO CONTINUE PLAYING WITH YOUR DEAREST REPLIES. THANK YOU MY FRIENDS FOR ENLIGHTING THE PATH TO ME* :) :) :heart :heart :heart

A final question before I end this page on the forum is that the arbiter talked to me rudely afterwards the tournament and supported the witness who was my opponent's father, So in the end of the day was the arbiter's behaviour shows a glimpse of her unprofessionalism or was I the person WHO WAS WRONG TO REPORT MY QUERY TO THE ARBITER

What can I do in that time because that tournament didn’t have the convenience of letting players write their moves over the score sheet. And *BTW I AM COVEYING A BIG GRATITUDE TO ALL THOSE WHO HAVE GIVEN ME THE WILL TO CONTINUE PLAYING WITH YOUR DEAREST REPLIES. THANK YOU MY FRIENDS FOR ENLIGHTING THE PATH TO ME* :) :) :heart :heart :heart
Well, if you can't record your moves during a tournament, then the tournament has a real issue with how move disputes can be resolved. If they can't have someone watching each board, ensuring that double moves are not made (as in your case), then really, they shouldn't be conducting an official tournament.
But that's another issue. For you, it is a matter of deciding what is important, and why do you enter tournaments? Personally, I would advise against caring about your rating. Once rating points "matter" to you, your chess will suffer. You will become a "rating points miser", and like a miser, your hoard of gold, never spent, will still leave you living the life of a poor peasant. Spend your rating point gains by trying a new opening, or entering a new line, be not afraid to lose those points you gained in your last game/tournament, because they are loose change in your pocket. If some jerk pulls a stunt like your recent experience at a tournament you entered knowing they couldn't monitor the games properly, then just present your side, and if it goes against you, consider it no more than the coins you may drop in the street by accident. Rating points are not "real", they should not be your goal.
As you improve, what will happen is that you will slowly gain more points than you spend because your income will exceed your expenses. Taking risks, trying new lines, or trying out a new "style of play" (if you are generally positional, try a tactical gambit line - if you are more tactical, try playing positionally - you learn by playing what you are not good at, and you are not good at what you do not play).
Basically, enjoy the game, for it can be beautiful. And, enjoy your tournament experience, for that is what it is, an experience. If jerks create chaos, you come away with a story, and you know what? More people will be interested in that story than will be interested in the moves of the game that was being played. It's life, so live it, and don't get caught up in the hype. Observe what is happening, play your part in the events, but don't forget, the part you play is your choice - nobody but you writes your lines.

A final question before I end this page on the forum is that the arbiter talked to me rudely afterwards the tournament and supported the witness who was my opponent's father, So in the end of the day was the arbiter's behaviour shows a glimpse of her unprofessionalism or was I the person WHO WAS WRONG TO REPORT MY QUERY TO THE ARBITER
You were not wrong. Unfortunately, your opponent had a witness who backed them, and the arbitrator would have little recourse but to side with the one that has a witness (although they could factor in the relationship between the witness and the player, and realise that there isn't an "independent witness" for either side).
However, if you were overtalking the arbitrator, as your initial post indicates, you may simply have not done yourself any favours by doing so. Again, should something similar happen in the future, focus on the goal (it's like trying to find that checkmate you know is in the position but just can't see yet). Stay calm, present your side both calmly and politely, and don't react if you think the arbitrator is ruling against you. Sometimes, they are evaluating your reaction, so react like someone who confidently knows they are in the right and doesn't have to interject with more (that looks like someone trying to convince, rather than someone who is convincing).
@15
"that tournament didn’t have the convenience of letting players write their moves over the score sheet"
++ A score sheet is mandatory, except for rapid and blitz:
'8.1.1 In the course of play each player is required to record his/her own moves and those of his/her opponent in the correct manner, move after move, as clearly and legibly as possible, in one of the following ways:
8.1.1.1 by writing in the algebraic notation (Appendix C), on the paper ‘scoresheet’ prescribed for the competition.
8.1.1.2 by entering moves on the FIDE certified ‘electronic scoresheet’ prescribed for the competition.'
A spectator is not allowed to interfere in a game. There is no provision for witnesses. The arbiter must observe himself or designate a deputee to observe in his stead.
'12.7 If someone observes an irregularity, he/she may inform only the arbiter. Players in other games must not to speak about or otherwise interfere in a game. Spectators are not allowed to interfere in a game. The arbiter may expel offenders from the playing venue.'
'A.1 A ‘Rapid chess’ game is one where either all the moves must be completed in a fixed time of more than 10 minutes but less than 60 minutes for each player; or the time allotted plus 60 times any increment is of more than 10 minutes but less than 60 minutes for each player.'
'A.2 Players do not need to record the moves, but do not lose their rights to claims normally based on a scoresheet. The player can, at any time, ask the arbiter to provide him/her with a scoresheet, in order to write the moves.'

@15
"that tournament didn’t have the convenience of letting players write their moves over the score sheet"
++ A score sheet is mandatory, except for rapid and blitz:
'8.1.1 In the course of play each player is required to record his/her own moves and those of his/her opponent in the correct manner, move after move, as clearly and legibly as possible, in one of the following ways:
8.1.1.1 by writing in the algebraic notation (Appendix C), on the paper ‘scoresheet’ prescribed for the competition.
8.1.1.2 by entering moves on the FIDE certified ‘electronic scoresheet’ prescribed for the competition.'
A spectator is not allowed to interfere in a game. There is no provision for witnesses. The arbiter must observe himself or designate a deputee to observe in his stead.
'12.7 If someone observes an irregularity, he/she may inform only the arbiter. Players in other games must not to speak about or otherwise interfere in a game. Spectators are not allowed to interfere in a game. The arbiter may expel offenders from the playing venue.'
'A.1 A ‘Rapid chess’ game is one where either all the moves must be completed in a fixed time of more than 10 minutes but less than 60 minutes for each player; or the time allotted plus 60 times any increment is of more than 10 minutes but less than 60 minutes for each player.'
'A.2 Players do not need to record the moves, but do not lose their rights to claims normally based on a scoresheet. The player can, at any time, ask the arbiter to provide him/her with a scoresheet, in order to write the moves.'
Interesting to learn some of the details. I played in only a couple of tournaments, and those many many years ago (in the 1990s).
I'm curious, though, about this rule, not because it matters broadly, but only because of my own idiosyncrasies:
8.1.1.1 by writing in the algebraic notation (Appendix C), on the paper ‘scoresheet’ prescribed for the competition.
See, I'm old, and I grew up with descriptive notation. I still "think" in descriptive, and when I've played OTB games with friends and get tasked with recording the game, I write it in descriptive.
Does that mean, in the hypothetical situation of me entering a tournament, if I were to record the game in descriptive notation, that my record of the game would not be considered valid? (or that I was in breach of the rules by doing so?)

Oh, and for those who don't know what I mean by descriptive notation, that's where things like:
1. e4 e5
2. nf3 nc6
...
Are written as:
1. P-K4 P-K4
2. N-KB3 N-QB3
...
there are pro's and con's to both systems, but that's another topic entirely.
@20
"if I were to record the game in descriptive notation, that my record of the game would not be considered valid? (or that I was in breach of the rules by doing so?)"
++ Indeed: descriptive notation is no longer valid. See appendix C:
"FIDE recognises for its own tournaments and matches only one system of notation, the Algebraic System, and recommends the use of this uniform chess notation also for chess literature and periodicals. Scoresheets using a notation system other than algebraic may not be used as evidence in cases where normally the scoresheet of a player is used for that purpose. An arbiter who observes that a player is using a notation system other than the algebraic should warn the player of this requirement."