Welcome to immigrationboards.com!
Unfortunately, you can only apply for your child's dependant visa if you have sole custody. Actually the rules say "... has and has had...", so even changing to sole custody now is unlikely to help.
Have you clicked on the links that vinny has provided (319H and (f))?? See also immigration-for-family-members/sole-res ... 13087.htmlPlease advise where exactly this sole custody clause and those words mentioned and where I can get the full details of the process even if it a difficult one. I wish to understand the procedure first.
If you have joint custody after divorce in the form of a court order, you will need to get the same changed giving you sole responsibility. Still no guarantee that you will be successful with the visa.Is there any FORM where the Mother can sign giving the sole custody of the child to me to allow applying for his visa.
A child born abroad usually qualifies for citizenship when at least one parent is applying for has already and the other parent holds ILR. The rules for ILR will be the same as for the PBS Dependent visa, the question of the other parent will be asked.Also, if I get ILR and later Citizenship, will the rules change to apply for his ILR and Citizenship as father with ILR/Citizenship.