Can I get a residency for my father?

Hello dstdce thank you for reaching out.
Congratulations on your permanent residency!
An application for family reunion is only possible for immediate family members, like spouses and minor, unmarried children. Unfortunately, your father doesn't count. In some countries, there is the possibility to apply for "other family members" but the hurdles and the proof for humanitarian reasons and financial support are very high. In which country is your father currently residing? To get proper support for such a case, it is recommended to get legal advise.
Happy to look for a migration counselling in your area. Would you like to share the city you are currently living or the next bigger city? Alternatively, you can also look yourself in the search mask of BAMF: https://bamf-navi.bamf.de/en/Themen/Migrationsberatung/
Happy to get some feedback. Feel free to get back, if you have more questions.