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In frequentist hypothesis testing, the $p$-value is the probability of a result as extreme (or more) than the observed result, under the assumption that the null hypothesis is true.
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p-value adjustment for correlation matrix
You can find the algorithm for multiple testing on correlation matrices that accounts for heavy dependence in Cai, T. T., & Liu, W. (2016). Large-Scale Multiple Testing of Correlations. Journal of the …
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What are correlations among between test statistics in multiple comparison procedures
This chapter is about the cases when some additional assumptions about the distribution of data are satisfied. For example, in linear regression setting due to the normality of errors the usial t-stat …
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Accepted
Does filtering of data by effect size violate some assumption of P value adjustment methods?
Yes, a filter like that indeed introduces bias to the multiple testing procedure, because the remaining p-values are no longer uniformly distributed on [0,1] under the null hypothesis. Here is a paper …