Does time dilation drop off like a gravity or does resemble a magnetic field model?
Could a smaller body with a magnetic field have more time dilation then a larger body without and to what degree?
There is a magnetic field whenever there is a moving charge, and since "moving" is a relative term, there is at least the possibility of some observer seeing a magnetic field whenever you have any charged object at all. However, there are thought experiments which show time dilation without involving any charge.
An example in special relativity would be a beam of Z0 bosons (which are, as far as we know uncharged fundamental particles). If the beam was moving fast relative to some observer, then they would appear to decay less quickly.
A GR example is an uncharged black hole (possible in theory, but unlikely in reality – any black hole will have a bit of charge, just by chance). A clock (our bunch of Z0 bosons for example) close to the black hole will seem to run slower according to a distant observer at rest relative to the black hole. The exact degree of dilation will be affected by the charge on the black hole, but it would have to be very highly charged for the difference to be much.