Would a matter-antimatter explosion cause fallout? I know matter and antimatter annihilation release a lot of gamma rays which are considered ionizing radiation if I am not mistaken. But what if the explosion happened on the surface of the earth, would the the material taken into the fireball cause fallout afterwards ?
My question in another form, what causes fallout ? and is ionizing radiation capable of radiating materials for a long time ?
 A: In a fission bomb, the fallout consists of fission-decay fragments, which are nuclei that can have long enough half-lives to be transported by winds. Fusion bombs are basically the same idea, because they use fission triggers.

and is ionizing radiation capable of radiating materials for a long time ?

In theory, yes, e.g., exposure to neutrons in reactors can be used to intentionally produce radioactive isotopes. In practice, although nuclear bombs must produce this kind of artificial transmuation of the surrounding matter (e.g., they do emit neutrons), I think there isn't enough of this kind of process to contribute noticeably to the fallout.
Matter-antimatter annihilation from a hypothetical macroscopic explosion would produce the same particles as proton-antiproton annihilation in microscopic quantities in accelerator experiments. You get high-energy (~100 MeV) gammas, medium-energy (e.g., 511 keV) gammas, pions, muons, and neutrinos. The neutrinos fly off harmlessly and undetectably into outer space. Matter is nearly transparent to the high-energy gammas; the downward-emitted ones are absorbed somewhere underground. The medium-energy gammas are absorbed in nearby matter. The pions and muons are unstable and decay quickly into stable particles such as electrons. Nothing long-lived is produced.
A: Antiproton proton annihilation is a strong interaction. It will last on the order of 10^-23 seconds. That would create a blast of energy but those atmospheric processes take order of milliseconds. Even if they take order of microseconds all the decays will have happened before any material enters the blast.
Anyway how much energy will be in the blast and how much will be radiated to space in the 2pi sphere pointing out to space  before leaving much of the energy in the atmosphere is a matter of detailed modeling. It might be quite possible that the energy will dissipate as 1/r^2 into the ground without managing to heat up the atmosphere enough to create a blast. So it could be just a sterilizing wave, killing live things in its direct path; note 1/r^2 is strongly dissipative 1000 meters away the effect goes down by 10^6. This applies also to any radioactivity from decay product interactions with the ground.
All this is a matter of detailed modeling but nobody will do it for you since it is impossible to create such a situation anyway. You should pick up a more realistic project.
