Issue with DOB in Birth Certificate

I am an expat living in Germany who originally comes from Kerala, India. I'm reaching out regarding an issue with my birth certificate. My date of birth on my birth certificate is different than that on my passport and all other official documents. This discrepancy arose because school officials commonly altered birth dates in the 90s and 2000s to extend service time eligibility for future public sector jobs. My passport application and other documents were based solely on my 10th-grade exam certificates, and this error has persisted. My current problem is that, I am currently on the path to apply for citizenship in Germany. But this requires my birth certificate. However, the disparity between the dates on my birth certificate and passport poses a problem. My questions are twofold: 1. If there is a way to get the birth certificate to be corrected? 2. If not, what are the steps I would have to follow to correct all my other documents? And is it even possible when I am living abroad? I would greatly appreciate any assistance or guidance you can provide. Please let me know what are my possibilities, if any. Thank you for your support.