Extending Global Talent dependent visa after it expire

Thank you for this useful forum! 

I hold ILR after 3 years on skilled worker and global talent visas. I have 2 kids who are dependents on my GTV (one born in the UK and one born outside). When I got my ILR, I applied for both kids for citizenship, the child born outside the UK based on the home secretary discretion option. No, I'm waiting for the decisions of their citizenship applications. My concern is that their visas will expire next week. My questions are:

1. If the child born outside UK's application is rejected, can he still extend his GT dependent visa even if it is expired?
2. If he can't extend his visa, what other options can he do?

Notice, they have been dependents on me for 7 years now (Tire 4 student visa, skilled worker visa, and GT visa).

Your insights in this urgent matter would be greatly appreciated.

Your child born abroad has no entitlement to register as British without ilr and your wife also holding ilr and at least one parent also applying for British citizenship.

Once their visas expire, they become overatayers. This isn't an issue for the uk born child though.

Thank you very much. Do you think it is possible to apply for visa extension now before it expire and waiting the decision of their citizenship application? or I can't have 2 applications in the same time (one for the citizenship and one for the visa extension).

Visas and citizenship are two different processes completely.

The uk born child doesn't need a visa though.

Thank you very much for your helpful information