Hello,
No private engineering colleges in West Bengal won't ask for domicile certificate while admission. It is only applicable for the government colleges for engineering.

Here's a list of some of the best private engineering colleges in West Bengal


https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/colleges/ranking/top-private-engineering-colleges-in-west-bengal&ved=2ahUKEwjArbTlj4_jAhXFQ30KHdnHC84QFjAEegQIBxAB&usg=AOvVaw2lpGpeSlHLrBjFszYR3nz7
Hope it helps