if someone purchases a fixed asset like car (f.y.16-17) in cash for personal use and does not want to claim depreciation on that will it be allowed or not or any impact in itr
No it will not impact since as you told it is purchased for personal use. in books of accounts that is not being shown then depriciation will also not allowed. cash purchase should be avoided , in business it will disallowed even for personal use cash transaction for big amount should avoided.
Asset for personal use will not have any effect. On the contrary if you purchase a business asset by cash, you cannot avail depreciation benefit w.e.f A.Y2018-19