Hi @Mankaa
Your child may be able to get a resident permit for Germany. For people with paragraph 25b, it is only possible for them to bring family members for humanitarian reasons. As the child presumably has also a temporary residence permit in Lithuania, then I do not know if the situation can be considered under humanitarian reasons. The father will have to show proof of paternity and custody and you will have to give your permission for the child to move to Germany. Even with all that, I do not know if the application would be successful.
Another requirement is that the person in Germany can cover the living and housing costs for the child. You write, however, that the person has 25b, Abs. 3. That section of 25b refers to people who are unable to fulfil the requirement of being able to financially support themselves due to age, illness or disability. If this applies in the father’s case, then it would equally apply for the child.
The German embassy has detailed information on the procedure and documents required:
https://wilna-diplo-de.translate.goog/lt-de/service/05-VisaEinreise/-/2632982?_x_tr_sl=de&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp
Here you can read generally about family members joining those who have 25b:
https://***-nds--fluerat-org.translate.goog/leitfaden/15-aufenthaltserlaubnis-nachhaltige-integration/aufenthaltsrechtliche-situation/aufenthaltserlaubnis-nach-%C2%A7-25b-abs-6-aufenthg/?_x_tr_sl=de&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp
Both links are in English via online translation.
Best,
Éanna