The magneto-electrostatic tailoring of the supercurrent in quantum point contact ballistic Josephson junctions is demonstrated. An etched InAs-based heterostructure is laterally contacted to superconducting niobium leads and the existence of two etched side gates permits, in combination with the application of a perpendicular magnetic field, to modify continuously the magnetic interference pattern by depleting the weak link. For wider junctions the supercurrent presents a Fraunhofer-like interference pattern with periodicity h/2e whereas by shrinking electrostatically the weak link, the periodicity evolves continuously to a monotonic decay. These devices represent novel tunable structures that might lead to the study of the elusive Majorana fermions.