Yes, the discrepancy between your father's name in your documents (Ramanraj Kumar) and the caste certificate (Raman Raj Kumar) could potentially cause problems during admissions to government or private colleges or when applying for jobs. Due to the following reasons :

• Verification: Government and private institutions often verify documents carefully, and any inconsistencies can raise questions.
• Eligibility: Some institutions or job positions may have specific requirements regarding the accuracy of names and other personal details.
• Legal Issues: In some cases, discrepancies in names can lead to legal complications.

To address this issue, you can consider the following options:

1. Affidavit: You can create an affidavit stating the correct name (Ramanraj Kumar) and explaining the reason for the discrepancy. This can be helpful in clarifying the situation and providing evidence of the correct name.
2. Correction of Caste Certificate: If possible, try to correct the name on your caste certificate. Contact the relevant authorities and follow their procedures for making the necessary changes.
3. Contact Institutions Directly: Before applying to colleges or jobs, it's advisable to contact the specific institutions and inquire about their requirements regarding name discrepancies. They may have specific guidelines or exceptions in place.

It's important to consult with legal experts or professionals familiar with the specific requirements of the institutions or jobs you're interested in.

I hope this information helps you.