Odd choice to cross-post this in Cacti & Succulents and Cacti Gallery. Anyway, the other day at a garden center I saw a product that you can spray on a tree to stop it from producing fruit. Unfortunately I can't remember the name of the chemical in the spray. Something that started with an E. Though, I think the spray is meant to be applied when the tree is flowering. I can't see fruits in your picture but I guess they are there. Otherwise I doubt you'd be asking about them. I think your tree is too far along in the process of producing fruit to be sprayed this year. I guess you could chop off the fruiting branches but if you are going to do that every time it produces fruit you just as well remove the whole tree and find a different ornamental that is better at not producing fruit.

Some ornamental cherries produce fruit. Best to leave it alone.

Looks like a purple leaf plum (Prunus cerasifera) rather than a cherry. And while considered an ornamental tree, it does produce fruit.....just not very edible fruit :-) And it is about the same size and shape as a cherry.....just produced much later in the season.

These are not considered particularly valuable trees (popular with developers because they are so inexpensive) so if you do not want to be bothered with any fruit, I'd suggest removal. Heavy pruning really disfigures them and will generate a mass of epicormic growth/water sprouts.