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    $\begingroup$ I'm thinking this is either not possible and not recommended. $\endgroup$ Commented Jul 4, 2018 at 23:47
  • $\begingroup$ As a workaround try this: ClearAttributes[Times, Orderless]; Times[x___, Subscript[a_, n_], y___] ^:= Dot[x, Subscript[a, n], y]. It will use Dot instead of Times every time a Subscript appears inside Times. It's necessary to clear Orderless attribute in order to preserve the order of arguments though. $\endgroup$ Commented Jul 5, 2018 at 2:43
  • $\begingroup$ @QuantumDot All the interesting things are :) $\endgroup$ Commented Jul 5, 2018 at 10:01
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    $\begingroup$ Why do you insist on using Times? Mathematica tends to be unpredictable sometimes. Based on past experience, I would not dare mess with such a fundamental built-in as Times. $\endgroup$ Commented Jul 5, 2018 at 10:37
  • $\begingroup$ Did any of the answers satisfied your need? There are things to do after your question is answered. It's a good idea to stay vigilant for some time, better approaches may come later improving over previous replies. Experienced users may point alternatives, caveats or limitations. New users should test answers before voting and wait 24 hours before accepting the best one. One weeks is enough wait. Participation is essential for the site, please do your part. $\endgroup$ Commented Jul 11, 2018 at 18:25