I am not sure what you mean by a prayer intention but I remember when I was a child my grandmother sending me to the presbytery (rectory) with money in an envelope together with a request for a Mass to be offered for the repose of the soul of my grandfather.
I ask father to offer Mass throughout the year for my relatives and here is Australia it is customary to give a $10 Mass stipend. I have also asked father to offer Mass for people who are suffering from cancer in the parish. I mention this to illustrate that Masses can be offered for the living and the dead.
As far as I am aware if you can’t afford a stipend and would like a Mass said for a particular intertion father will do this.
In the UK we would pay Father to have a Mass said for someone a voluntary donation.
To ask for a prayer intention to be mentioned at the bidding prayers there is no money involved.
At the Prayer intentions forum here are many prayer warriors and if you need prayers we are always happy to join you in prayers.
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