Dropdown vs Modal for table header filtering

I am trying to filter data in tables by converting each header into a split button. Left part of the button will sort the data on click while the right part opens a dropdown at the moment. It looks like this currently enter image description here

It also seems that there is a possibility to open that area in a modal. I couldn't find any practices for modals vs dropdowns when it comes to table headers.

  1. One problem I noticed with dropdowns is that they get a little clunky in the mobile view
  2. Another problem is I have a dropdown inside my dropdown. Is this an acceptable UX thingy

enter image description here

Can someone kindly help clarify the right approach for this