When an electric charge flows through space, an electromagnetic field is produced.
A magnetic field and an electric field combine to form the electromagnetic field. Because it propagates at the speed of light, the electromagnetic field can be characterized as light.
The interactions of current and charges with the electromagnetic field are described by Maxwell's law and Lorentz force law.
The magnetic force direction is determined by the direction of the current and the magnetic field.
Right-hand thumb rule:
If a current-carrying conductor is imagined to be held in the right hand such that the thumb points in direction of the current, then curled fingers of the hand indicate the direction of the magnetic field.
If the current flows in an upward direction then the direction will be anticlockwise.
If the current flows in a downward direction then the direction will be clockwise.
Therefore, the charge moving with a uniform velocity produces the magnetic field.