Q:

If my characters can control electrons could they use this as a means to attract and repel objects?

Could they use their abilities to change an objects electromagnetic fields to work in their favour.
I want my magic system to be explained as the story progresses. I’m thinking this could be a way to explain telekinesis? If this sounds plausible would they be limited by their size i.e. only able to manipulate objects a fraction of their size?

A:

the Basics
Short answer yes.
https://courses.lumenlearning.com/boundless-physics/chapter/magnetism-and-magnetic-fields/
Well we know from Amperes law the relation between a magnetic field and the current pathing through the surface of that path. In short you can create a magnetic field with a current of electrons moving in a circle.
In a second step you can use the Lorentz law to induce an internal current in an object while creating a magnetic field through more electrons moving outside the object to create that field. This will get your object moving.
There are however drawbacks with this 

Not all objects are very good conductors (having many free electrons) so creating a current in them will likely damage them
The magnetic fields you will have to create are somewhat complex depending on the situation, yet you have to go through electrons to create your magnetic fields

diamagnetic levitation
That said if your outer magnetic fields are strong enough and have the right form you can repel diamagnetic objects. Even biological ones.
https://www.ru.nl/hfml/research/levitation/diamagnetic-levitation/
paramagnetic/ferromagnetic levitation
Will require less strong fields to get done. The principle is the same as with diamagnetic materials though.
creating currents magically
Is dangerous ... your power is more of the I can electrocute you with my mind kind, rather than I can levitate you.
Also as all materials will have some sort of resistance to you moving your electrons through is bound to cost you energy as the perpetrator.
Limitations of your power very much depend on the energy you can exert and what your powers can move. 
A lot of what I said becomes void when you can move electrons trapped even in the potential of atoms. I would not suggest this however but only limit this to those already free roaming electrons.
As you are moving millions of electrons simultaneously you will have to have an impressive brain capability.
conclusion
You are 

A super computer moving single electrons to your whim
You have to eat a lot to conserve the energy
You are close to god hood and Maxwell wants to have a word with you!

