What is the ruling on giving a percentage of money to an employee in an entity that requests a study, in exchange for him hinting at such, knowing that the amount will be from special bonuses and will not affect the quality of the work?

If studying is a right of the questioner, and it can only be obtained by paying a bribe, then there is no harm in paying it, and the sin is upon the one who takes it. However, if it is not a right of the questioner, but rather subject to the choice of the entity requesting the study, then it is not permissible to pay a bribe under any circumstances.