Need advise on laws

Uae laws don't apply in Bahrain, it's a different country after all.  Inheritance is governed by Shariah law and is based on recognized relations ie marriage.

Secondly, I doubt if you will have any luck pursuing it in the courts. The marriage was never registered in Bahrain and to establish birth out of wedlock in a foreign country, which happened decades ago, is not likely to gain any traction.  You can contact a lawyer and get proper legal advice to pursue this further.

In my view, it's probably better to file against him in the UK. So if you ever have a positive outcome, you can hold him accountable whenever he visits UK.

This doesn't sound promising at all

Unfortunately it isn't. None of the GCC countries recognize birth out of wedlock. In fact, if it happens here, people end up in jail and expats get deported / banned.  So claiming rights after this is exceptionally difficult... More so when the birth happened outside of Bahrain and on top, 30 years ago. That's why I said to file in the UK.