Simple finger strength building exercises:
Use your 1st, 2nd, 3rd and 4th fingers. With these exercises same finger number as the fret you are playing.
Expand each exercise by playing the same pattern through all six strings.
Use ‘Alternative Picking’.
Start slow, get a clean sound, don’t snap at the note.
Try and stretch but don’t force yourself to do something you can’t physically do yet.
If when playing the 3rd or 4th fret your 1st finger moves then so be it, eventually with time your fingers will adapt.
These are warm ups, treat them as such. Use them to develope your finger strengh but don’t spend too much time on them.
Save that time for the fun stuff.