Thanks for your question. I will try to help.
Unfortunately, I do not think your son is eligible for a UK passport.
The most optimistic scenario would be that your mother obtained UK citizenship “otherwise than by descent”. Even this is still unclear on the information that you have given me.
If she had this citizenship (ie. the most useful in terms of passing to children) then because you were born outside the UK you would have inherited it from her “by descent”.
Unfortunately, this means that you cannot automatically pass your citizenship on to your children if they are born outside the UK. The only way that your son would have been able to apply for UK citizenship would be by registering him whilst he was a child. In order to do this you would have to have shown that you are a UK citizen by descent and that you spent three years in the UK at some point before he was born and that you did not leave the UK for more than 270 days within this three year period.
However, because registration in these circumstances would have to occur before the child is an adult it would not now be possible for him to register as a UK citizen because he is an adult. This is very strictly applied.
This means that if he now wished to naturalise as a UK citizen he would have to go through the same process as any other non-UK, Non-eea citizen, which means that he would have to secure a visa which allowed for him to work in the UK and then live her on that visa until such time as he is able to apply for “indefinite leave to remain” (usually 5 years) and then apply to naturalise 12 months after obtaining indefinite leave to remain.
I am really sorry that I could not have better news for you
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