Hi Vivek,
If it was a case registered against you & fine was paid as court order, then it is documented & the record will remain. If it was just a fine at street/station & just receipt was produced, then it will not have long term record for such background verifications.
The time frame would also be important. If the conviction was recent, then police may remember it & create an issue for the verification certificate (if applicable for type of visa).
Though, some countries have very strict verification checks for "resident visa"; For most of other countries & business visas / short visit visas, the process would be lenient.
On a little different track, .....It is unfortunate that educated people like us tend to ignore the basic rules of life (be it a law or not), until they affect at a life changing decision. All readers of this blog should take this example to understand, that even small mistakes can make you vulnerable at most crucial point of life; & hence we should all be vigilant to keep away from such "avoidable mistakes".
Best Regards,
Amod Bobade