Welcome to the forum
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Unfortunately, fiance visa is a settlement visa and therefore the Super Priority Service is not an option for you. The reason for this is that settlement visas (fiance/spousal visas) are not processed in New York, they are processed in Sheffield, UK and are only processed by mail.
You will need to mail your application to Sheffield for processing, and your only option for speeding up the process is to purchase the 'Settlement Priority Service' for £450 ($653) on the VFS Global website. This will get your application put to the front of the processing line (behind other priority applications, but in front of everyone else) so that it is opened and looked at quicker.
I would allow a few weeks for the whole process to get the visa, especially as we are going into summer now and the processing times tend to slow down a bit (last June/July it was taking about 1 month for priority processing and up to 3 months for non-priority processing).
The online application should be the LAST thing you submit after you have checked that you meet all the requirements, gathered all your documents, and printed and filled out the second half of the application form - VAF4a Appendix 2.
You can see the paper version of the online application form for reference (VAF4a) and also print off the Appendix 2 form here:
https://www.gov.uk/government/publications/application-for-uk-visa-for-family-settlement-form-vaf4aHave you made sure that you meet the requirements:
1) Financial requirement: your fiance makes at least £18,600 in the UK and he has evidence of this by way of payslips, bank statements, a letter from his employer, his job contract and his latest P60
2) Accommodation requirement: you have evidence of somewhere to live in the UK, with written permission from the homeowner (if your fiance doesn't own it)
3) Relationship requirement: evidence of regular communication between you - visits to see each other, regular email/phone/message contact for the last year
4) Evidence of plans to marry in the UK: i.e. a provisional booking for a ceremony within 6 months of the fiance visa starting, correspondence with the church/registry office etc.