I believe the term you’re looking for is a stipend. The amount depends on a few things (ie: private or communal baptism, etc.) Ask your parish office what the typical amount is, but again, it’s more of a guideline than anything.
In our diocese the priest receives a stipend for baptisms from the parish, unless a family brings in their own priest. In that case I would offer them a stipend. But if it is the parish priest what you give them would be on top of what the parish gives them. We give our parents a donation envelope at baptism and say they can donate whatever they want (and some do give nothing). Many parents think that donation goes to the priest but it goes to the pastor who then distributes it to the priest celebrant of the baptism and for the baptismal supplies.
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