I did a two-way mixed ANOVA for my variable and got some significant result. For post hoc tests I am suppose to perform a independent t-test but against zero which I am a little confused about. Any help would be appreciated.
The specific method depends on which effect you're following up (in your mixed design, there are three effects: main effect of the between-subjects factor, main effect of the within-subjects/repeated measures factor, and interaction of group x measures). Here's a source that you may find helpful:
what do you mean with "perform a independent t-test but against zero"? Maybe your confusion comes from this formulation. Technically speaking it is absolutely correct, since the Null-Hypothesis is µ1 - µ2=0, so you are testing, if the mean difference between two groups is zero. But if you put it another way, you want to know if the mean values of the groups differ. So, from this point of view, you are not testing against zero, but two mean values against each other (but which in turn is essentially testing against zero...).
t test for post hoc anova comparisons is wrong, you must to read something about post hoc tests or multiple comparisons, the selection of a particular test depends of the objectives of your research. I recommend you this paper: