Overview of different tests

Moderator analysis 

A moderator analysis is used to determine whether the relationship between two variables depends on (is moderated by) the value of a third variable. It is often also referred to/closley related to interaction. 

For your analysis, make sure you include an interaction/moderation term of your independent variable and another third variable. Another posssibility for the analysis is the tool PROCESS. You can download the software for R and SPSS here

Please read this article to figure out whether you are aiming for a moderation or a mediation analysis. For more information about mediation see here

In the video below, you find a more detailed explanation of moderation analysis.