have you practiced in psychiatry in your home country recently? when was the last time you were working as a physician? If it wasn't in the past few years, you have no chance of matching into psychiatry and there is nothing that you can do to improve your chances. If you are already a psychiatrist and have practiced recently, then you have a small chance of getting into residency in the US. You need to think about alternatives, whether that be alternative careers (such as training and practicing as a therapist or psych NP) or seeing about working in other countries. Unfortunately, with the increasing number of US medical students, and a small increase in the popularity of psychiatry, it is increasingly competitive to match into US residency, especially psychiatry. Most places won't consider someone more than 5 years out of medical school. Your scores are very low for this era (not clear when you took the USMLEs, but today a 198 would not even be a passing step 2 score so it must have been years ago).
It sounds like you have worked very hard to get things like publications and externships etc to be best placed to match, and have not been able to do so. We can sometimes tell ourselves "if only I do x, then I will be able to...". But that doesn't apply here. You had your chances to match, and unless you have very recent clinical experience (not an externship or observership, really clinical work), and a good relationship with someone in a position of influence to advocate for you to get a residency spot, it isn't going to happen and there is nothing that you can do about it. It's very demoralizing and not want you want to hear, but it is the truth. I am an IMG and have supported many IMGs over the years. We had 2 IMGs with much higher scores than you, only 2-3 years out from medical school, with research experience, and who rotated with me and got letters from a top academic institution and neither of them matched this year 🙁 It is only going to get harder for everyone. I don't want to discourage IMGs in general (as 1/3 psych residents are IMGs) but someone this far out of medical school, with barely passing scores from years ago, no recent clinical work, and failed to match three times already has an almost irredeemable application. Nobody will want to take the risk on you when there are many more "safe bets" to choose from.