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i am sorry to hear about this situation. Please, clarify:
1) What visa were you applying for?
2) What is your nationality?
3) What specific ineligibility did the US Consulate/Embassy cite? In other words, what was the reason? If they simply provided a statutory code (a string of numbers/letters), let me know what that is and I can look that up. Thanks.
This is not an answer, but an information request. I need this information to answer your question. Please reply, so I can answer your question. Thank you in advance.
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The reason for denial was because you are considered a high risk for overstay due to your indefinite leave in UK and Ukrainian Citizenship (the US wants you to apply from your fixed, permanent place of residence and that both countries be stable - Ukraine is not in the East, right now). As such, you were denied under 214(b) - the suspicion that you would overstay your visa if granted.
ONCE you have UK citizenship, the US is much more likely to allow a visa. This includes ESTA/VWP, since you would not longer be considered an overstay risk, likely.
NOTE, that ESTA/VWP is more or less all automated. Any little thing can make ESTA deny, so there is still a chance that you may be denied ESTA with a UK Citizenship given your overall history. But a B1/B2 visa (or whatever else) would be likely granted once UK Citizenship is established.
As they say: "Щасти!"
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Thank you for your call request. The site allows the expert to opt out of the call request, and I must respectfully ***** ***** not worry - other experts receive the request as well, and the first available expert calls. They will also have your question and my replies to build upon, so nothing will be lost. You should receive a call in the next 5 minutes.