World championship for 960 and alternative version of chess

Is there world championship for chess 960 or any another alternative version like the queen can move like knight too and so on>?

no

The major Chess variants, such as Chinese Chess (Xiangqi), Japanese Chess (Shogi) and Thai Chess (Makruk) all have their own World Championships. Superchess does have its own Dutch national championship.

There is 960 world championship. Most masters play it regularly, including Nakamura (who was/is actually a 960 world champion), Aronian, and so on.

I wouldn't call Xiangqi and Shogi chess variants but games in their own right.

The chess960 "world championship" was a rapid tournament held by a single organiser unrelated to FIDE. It hardly deserved its designation. It was discontinued 6 years ago.

Xiangqi, Shogi and international Chess are all Chess variants. You could call any Chess variant a 'game in its own right', and ardent players of Gothic Chess, Seirawan Chess etc. would probably even agree with you. But a fact is that they are all minor variations on the same theme.

The difference is that FIDE Chess, Xiangqi, Shogi &c are descendants of a common ancestor (chaturanga or an older, unknown precursor), while Chess960, Seirawan chess, bughouse and all the others are based on FIDE chess. So I prefer to keep them apart.

But in the end it's a matter of opinion if you use the word  'chess' to describe the entire family of board games (as you seem to prefer), or if you use this word in its common meaning (as I am doing).

The danger is in the phrase 'all others'. The variants you mention certainly have strong FIDE roots. But that doesn't mean there aren't any modern variants that differ at least as much from FIDE as FIDE differs from Xiangqi or Bughouse differs from Shogi. Such as Great Shatranj, or Chess with Different Armies when you play the Nutty Knights against the Colorbound Clobberers armies.

The point is that it doesn't really matter what we consider Chess variants or games in their own right, but what the original poster did. It was not clear to me that a game in which the Queen-Knight compound he mentions would participate should be more FIDE-like than, say, Chu-Shogi like. It seemed rather obvious to me that when someone asks for 'alternative versions of Chess', he does not mean Chess in the 'common' (I would say 'narrow') meaning of FIDE Chess, as the whole subject of his question would then not exist. His posting makes it clear that the fact that pieces move differently does not stop him from still referring to it as 'a version of Chess'.

The western chess fide , (thai chess) makruk  ouk(camboya),  Xiangqi,  Shogi, Janggi, Sittuyin are descendants from  Shatranj   and shatranj is a descendant from   Chaturanga. They have his own championships. Others (960,  berlinga, etc)are modens forms of fide western chess

I guess the tendency exist to consider a Chess variant popular enough to have its own World Championship a "game in its own right". This would then make what the OP asks for by definition impossible...

Note that 'Shatranj' is merely the (ancient) Persian/Arabic word for 'Chess', and that 'Sjatranj' and 'Chess' are different wordsis not because they are different games, but because Arabic and English are different languages. I don't know the origin of the word 'Chess'; in Dutch the modern game is called 'Schaken', in German 'Schach', all derived from the Persian word 'Shah' = King.