2D Screen Particle Animations Help?

I've noticed in games that particles have been created across a player's screen. These aren't particles from an emitter or a 3D particle from a server script, but rather a client-sided script that displays floating particles in a player's screen.

I heard that I could use a player's camera:WorldScreenToPoint/WorldViewportToPoint via a loop and make particles based on the return position. However, the problem is that the position will stay the same and these games have it where movement is not required for animated 2d particles.

I was wondering how is it possible to go about this? Is there an algorithm? Should I make my own? Is it actually a hidden emitter?

I want to know how to go about this so I can create better UIs with better aesthetic appeals for the player. Especially after reading about Project Valkyrie, I want to make a game that really appeals to players in the smallest ways.

Thank you for reading and replying if you do.