How to ask for employment help or referral from someone you don't know? I will use fake names for the sake of anonymity. I have recently completed my PhD and applied to a professor position at University ABC. It has been almost 3 months since my application and I sent out an email to the Chair of the department (who presumably is the person in charge of recruiting academic/faculty members) but did not receive any response. There is another senior faculty member at University ABC, Dr. M, whose research is similar to mine and whose work I have referenced in my thesis. Moreover, Dr. M also attended the same university as my academic supervisor but they have never formally met.

Dr. M may not be involved at all in the recruitment process. However, I would like to ask for Dr. M's help in case he is able to give my application a push.

I am not sure how to write an email to Dr. M to ask for his help in such a scenario since there is no reason for me to believe that he is involved in the recruitment process. Nevertheless, I do want this job and I wan to do everything I can to make sure my application gets properly considered. How can I go about this task?
The typical approach is to send an email saying something like:


  Dear Dr. M.,
  
  My name is ... and I am applying for the position of ... in your department.  (Brief summary of your professional background and research interests.)  I am particularly interested in the position because I would look forward to the opportunity to collaborate with you.  Please let me know if there's anything you want to discuss.  My CV is attached (maybe also a preprint).


This alerts Dr. M to the fact you are applying, so that he can get in touch with the search committee if he wants to support your application.

However, normally you would do this at roughly the same time as you submit the application.  You say you applied three months ago, but when is the application deadline?  If it hasn't passed yet, or if it was just a few days ago, then there might still be time for an email to Dr. M to have some effect.

But if it passed some time ago, then the search committee has probably already finished one or more rounds of screening.  If that's the case, and you haven't been invited to interview or otherwise contacted, then unfortunately, you probably didn't make the initial cut.  In that case there is very little that Dr. M can do, so not much point in contacting him.

(By the way, it's pretty much irrelevant that your advisor went to the same university as Dr. M, if they haven't otherwise been in contact.  That kind of relationship is roughly comparable to this one.  So I'd leave it out of any message.)