Hi Camilo, We use "at" when the border is a point in a journey. "On" is used when we have a static location.

I will meet you at the border. (at the Mexican border) My hometown is on the border of Mexico. (on the Mexican border)

A place is on the border: "Gretna Green is on the border between Scotland and England"; "Tijuana is on the Mexican border" [seen from a US POV]. People are at the border: "They checked our passports at the border". In some contexts, you may use other prepositions, for example "in": "The artist drew patterns in the border of the print"; "Peonies were growing in the herbaceous border".