Bayesian inference field: given a dataset, if I assume a normal a priori distribution on the average parameter with zero mean and a given variance, those hypothesis tests can be carried out on the posterior distribution to assume (with a certain confidence level) that is the average really zero? Does it make sense to apply the t-test statistic on a posterior distributions (t.test in R) or is the t-test an exclusive hypothesis test of the sample media?
It does not make sense to apply a t-test on a posterior distribution - a t-test is applied to do data (although you could represent a prior through pseudo observations and then do a frequentist analysis such as a t-test).
One would more typically do one of the following:
look at how much posterior mass there is on the parameter being exactly zero (with a normal prior that would be zero, but you could create a point mass at zero in your prior - but see Lindley's paradox - or you could look at the posterior mass in an interval around zero that includes values that are in practical terms more or less zero)
Bayesian model averaging between models with the parameter set to zero vs. not set to zero
look at posterior credible intervals for the parameter (do they include zero and exclude values that are meaningfully different from zero?)
look at the Bayes factor between a model with the parameter to be estimated versus the parameter fixed at zero
Which of these makes the most sense may depend on what you are trying to do.