Signing/verification between Java and the OpenSSL
Your problem is not with the signature scheme, something else is wrong.

RSA is specified by the RSA cryptography standard, PKCS#1 (mirrored in various RFC's). The PKCS#1 v1.5 padding was introduced in version 1.5 but it persisted in 2.0, 2.1 and 2.2. Those did however introduce a more secure padding scheme called PSS.

Unfortunately nobody calls the signature generation schemes by their true name: RSASSA-PKCS1-v1_5. Both your C code and your Java code seem to use that signature scheme.