There might be a minor issue during the SSB document verification process for NCC entry due to the missing father's caste in your Class 10 (A) certificate. However, it is  likely manageable.The priority during verification is to confirm your identity. Since your father's full name appears in both your Class 10 (A) and Class 12 (B & C) certificates, this establishes a strong connection. Proactively address the issue. Discuss it with your NCC Unit officer. They might be able to provide a document stating that the missing caste information in your Class 10 (A) certificate doesn't create any discrepancy.

I hope it helps!