Yes, you can try applying for German Resident Permits based on Family Reasons, the German Law States that Family Members of those who have a Permanent Resident Permits or Settlement Permits Can also Apply for German Resident Permit in other to be able to successfully reside and stay with thier family members. the Family members who are qualified for this are e.g
(1)Spouse of a Person with a German Permanent or Settlement permits, even those with limited Residence Permits as far as they are lawfully residing in the Federal territory of Germany
(2) minor Childrens of a Person with similar permits listed above as far they meet up the requirements
(3) adopted Children of a person with similar permits also.
YOU CAN FIND IT STATED BELOW HERE IN THE GERMAN LAW. I WISH YOU GOOD LUCK
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Berlin
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Migration und Integration
Residence permit for spouses, parents and children of foreign citizens
Residence permit for spouses, parents and children of foreign citizens
Issuance or extension of a residence permit for
The spouses or life partners of the same sex of foreign residents with a valid residence title,
Under-age, unmarried children of foreign residents with a valid residence title,
Parents of foreign children with a residence title pursuant to § 23 para. 4, § 25 para. 1, § 25 para. 2 or § 26 para. 3, if no parent with an entitlement to personal care is a resident of the Federal Republic of Germany, and
Parents of foreign children with a settlement permit pursuant to § 26 para. 4 (if a residence permit pursuant to § 25 para. 2 s. 1, 2. Alt. had previously been issued), if no parent with an entitlement to personal care is a resident of the Federal Republic of Germany
Portal
Berlin