My step son is in Ark. Where his girlfriend has up and left to Alaska for the last 8 days and has said she is coming back for the 4 kids they have had together and take them back to Alaska my question is he is on the birth cert. as the father of the children and can she just come back and snatch them like that.

Has paternity been established BY A COURT?

I don't see an abandonment issue here - she appears to have left them with their father. Abandonment is sort of like leaving them at a bus stop.

What does he want to do? If he wants custody of the children he needs to go to Family Court NOW and request sole custody. He must do this NOW, explain the urgency of the matter and request that it be heard as quickly as possible.

At the moment she MIGHT be able to leave with the children.