Okay, so the issue is primarily that the shape of the lower case q, with a descender, makes it looks almost level with the 2nd level subscript 1. If you look at the base of the second level subscript 1, it is clearly lower than the bottom of the "loop" in q.
So what you need to do is to modify how much the subscripts are lowered. You can control this by setting \fontdim for the appropriate lengths. A discussion of how this works can be found in this post.
To illustrate the method, see the following code:
\documentclass{article}
\makeatletter %%% These three lines are to ensure the math fonts
\check@mathfonts %%% are configured prior the call of \fontdim. Include
\makeatother %%% if you run into an error about \nullfont.
\begin{document}
[ x^{q_{1_1}} ] %% Standard format. For reference.
\fontdimen16\scriptfont2=3pt % <--- This is the line that sets the height.
[ x^{q_{1_1}} ] %% Same expression, for comparison.
\end{document}
The output (top line is original, bottom line is with the increased subscript height):

You will have to play around with the parameters to find what makes you pleased aesthetically.
raisebox. – oliversm Sep 10 '20 at 16:23\raiseboxcommand. http://www.emerson.emory.edu/services/latex/latex_148.html But I doubt you would want to do it manually everytime you run into this. – Willie Wong Sep 10 '20 at 18:00\raisebox? What is the package ? – learner Sep 10 '20 at 18:12