Offered job - Asked for CURRENT reference but I plan to leave ASAP

R

Hi all,
So, I applied for a job back in november, got an offer recently and have been asked to provide references for pre-checks for the last few years.

Background, i decided to start a masters last year as job hunt was very difficult, and thought it would be good to do something while still applying for jobs. Now, when I applied for this job I didnt put the current masters course down as at the time I just started, and had no progress to show in terms of the project, and didnt want it to seem like I was a slow learner. In addition, I was planning to give a notice if I ever did land a job during the course, so that was in the back of my mind too.

Again, I didnt mention the masters in my application at the time, and now that they ask for "current establishment" I am unsure whether to add the masters.
Before any offers, I met with my supervisor and asked whether they would be a reference for any prospective job, and they essetially threw it back at my face and implied that I have not done any work since arriving, and that a reference is out of the question as "they cant lie". Just want to make it clear that it is not true at all, and at no point was I ever told that the work I was doing was incorrect or that I should speed up things at all, and again it has been only a few months since I started.
Overall my supervisor is being incredibly tough on no merit at all, and it makes me want to just completely leave out the course in the form. i dont want to reference someone who wants me to fail.
At this point Im strongly considering handing in my notice in as soon as I can, I cant work at the best of my ability when I have a supervisor who does not try to guide me at all, and belittles me at the first mention of an excellent opportunity.

So my questions:
Is it okay to not include the current course as a reference at all, given It's not in my CV either? What are my options here?
I want to remain consistent in my application, should I ask the HR of the offered job what to do without mentioning specifics?
Can leaving the course out of the references come back to bite me for later clearance checks (security)?

Please advise as I am in a constant mode of panic at the moment, unsure how to proceed as I do not want to jeporadise my chances at all.
Cheers
when I filled this out (months ago), I didn't contact my current employer for a reference because I know graduate schemes are tough to get on to and didn't want them to think I was leaving as I didn't even know if I would get a graduate position. It would have better to put a previous employer but didn't have the option.

What's best to do in this situation? I have zero clue what to do at all and I am severly worried I've ruined my chances.

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