(expanded from an earlier comment) Nearly always (and I only include "nearly" in case there are exceptions), when applying to U.S. universities you are explicitly asked to list all colleges/universities you have attended and those (if any) you are currently attending. You are also nearly always asked to provide transcripts (i.e. list of courses, when taken, grades if any received, etc.) from all such colleges/universities attended, this regardless of whether you earned a degree there. The transcripts usually have to be official (often means having to pay for them), but in the initial screening process personal photocopies/scans might be OK. That said, see also the last paragraph below.
In a comment you state that, when applying, you had not completed a single semester of the Ph.D. program and thus did not have a transcript there. Actually, I think "transcript" includes courses currently being taken, and I think the places you are applying to intend for any currently enrolled courses to be included. You also said that you have now completed that semester. I think you should contact whoever you sent the application to with this information, or whoever you received the acceptance letter from (if different). Since they have already admitted you, I suspect you will still be admitted unless there is something troubling in the completed courses, such as poor grades or some kind of disciplinary or academic concern indicated in the transcript.
You might want to explain that you did not think your current courses were intended, but before you do this, make sure that you carefully examine the exact wording of the application instructions pertaining to this so that you don't directly contradict something that is clearly written in them. My guess [= hunch; conjecture] is that you do not want to use more than two sentences doing this. Also, if you decide to explain why you overlooked this (i.e. if you say something beyond simply that you were not aware that current courses should be mentioned), such as for admission to India universities one would ordinarily not include not-yet-completed courses (I don't know if this is true or not, by the way), then make sure what you say is consistent with any facts that they might have access to and that it does not present you in a negative way. For example, regarding "does not present you in a negative way", if you say that you did not notice something in the application instructions, and that "something" happens to be in large bold-face font, then the admissions committee might view this as evidence of a lack of attention to detail or as an English reading proficiency concern.
Of course, now that you have brought up the fact that you have been in another Ph.D. program, you should also devote a few sentences to explaining why you want leave and study elsewhere. You should avoid saying much bad about where you are, even if it is bad in some ways. Instead, focus more on the "additional opportunities you now realize would be afforded to you in their program" (made-up flowery wording for illustrative purposes), such as ... (give some specifics -- e.g. better labs, opportunity to research Topic X which is not possible where you are at, advice from friends/advisors in your field, etc.).
In the above remarks I've assumed that courses were actually taken, with official records kept. For many non-U.S. universities, as Ander Biguri points out in a comment, there might not exist courses and/or semesters and/or transcripts. In these cases I'm pretty sure U.S. universities would still expect applicants to list any academic programs (in a general sense) that the applicant has attended or are currently attending. Although this does not seem to be the case for the OP, others in a similar situation may need to modify the remarks above as appropriate to their specific situation.