This is a professional problem, of a type that sadly can floor many students, because they have not been particularly exposed to formal institutional regulatory and political structures. This can be particularly true of older postgrads (in some senses more experienced), because those are the ones who have been most firmly focused on academic work all along.
For me, the hinge of this problem seems to be, ‘He seems very nice to other people, just not to me.’ That statement stands out especially because it means that the situation therefore involves bullying and harassment (succinctly defined on this UK site). You are being singled-out for ill-treatment, by someone who is not simply ‘like that’ to everyone. It seems that that person is quite immature, deriving satisfaction from such behaviour, and is also consciously selective in where to apply it.
The mature, professional solution will not be to fight back. That would simply resolve into immaturity on your part as well, and will not teach either you or the bully anything useful. Most likely, the bully would smoothly ridicule your behaviour, and use it as licence to continue his own. Pointless, and also unprofessional on your own part: do not go down that route. You can learn something much more useful for the future, by exploring the resources that I am sure already exist for you.
In a strange way, this situation is not all bad. Of course it is horrible for you to experience, but it also means that the problem is well defined. In this day and age, I would bet quite a lot that your university will already have a policy in place concerning bullying and harassment, with established procedures for reporting and controlling such behaviour.
Others here have suggested various ways of more or less taking this conflict on, on its own terms, and trying to win it. I think that that would be the worst possible thing to do. That would amount to you approving the bully’s behaviour as acceptable in your culture. In doing so, you would become as unprofessional and immature as he is. You would also waste a great deal of time and energy, while achieving absolutely zero.
You need to end the conflict, not take part in it. As has also been said, the bully has infinite energy: he likes doing this. As we say in the UK, he is trying to get the rise out of you. If you respond on his terms, he will just keep doing it.
What he cannot fight is you being calm and professional.
I would say that your first stop should be talking to your Ph.D supervisor, if you have a confident and trusting relationship. They should be able to point you at the University’s policy on bullying and harassment, which will clearly tell you how to proceed within the University’s existing framework (politely negotiating, collecting evidence, building a case). Also, it would be sensible to alert your supervisor to any undue influences that might be negatively affecting your work. This probably won’t be the first time they have seen some kind of friction, and it definitely won’t be the last.
If you don’t feel that comfortable (yet) with your supervisor, then that is fine. The University almost certainly has some kind of confidential Counselling service[s] for students and/or staff (you might count as both), which would be able to guide you towards the same formal resources, and discuss how to use them. If it offers no such dedicated service, then the University must have some kind of health centre, which could set you on the same path.
Another route could involve directly approaching the University’s HR office. They will probably be the guardians of the institution’s policy on respectful professional conduct, and will have an interest in seeing it applied consistently across the institution. There is a good chance that this is where you will end up anyway, if you start off with your supervisor or a counsellor... but I would recommend calmly and quietly going through those steps first. Those people are there for a reason. Both you and the University can benefit from making full use of their knowledge.
In any case, the likely first suggestion would be politely to make your colleague clearly aware that he is distressing you, telling him why, and asking him to stop. Of course that is a stressful step to take, in itself. The up-side of that is that occurs within a framework (the broader policy) that will provide routes for you if he responds unsympathetically or even aggressively.
More likely, the bully (immature as he seems to be) would seek to continue targeting you in ever-more-obscure ways. The great thing about that would be that by that stage he is on record as the aggressor. It is up to him to show that he is taking the University and its policies seriously. He might even argue angrily that you are being oversensitive and thus damaging his work, but by that stage the point is that he still has to be the one to show that he is taking steps to make things better. He has to grow up a bit and start really being professional, otherwise he will just keep getting warnings, drift into the University’s disciplinary system, and eventually get thrown out.
By the sound of it, he might not last long as a research student anyway. In the UK, the term ‘tosser’ would quickly be applied to someone who was that concerned to satisfy his own ego problems by spending time and energy picking on someone else, rather than excelling in his own work and collaborating with others.
Basically, keep calm and explore formal routes. They will exist.