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Do you earn more than £18600 per annum from salaried employment? This is part of the financial criteria..
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The short answer is that you really need to instruct a solicitor in person in order to advise you and then submit the application on your behalf.
The overstay is a problem in that the home office would initially reject the application because of this. You would then likely be forced to appeal and it is therefore very important to ensure that your original application is as good as it can be and contains all information that will be used on appeal.
Without child I would say that the best way forward would be for an out of county spouse visa application to be prepared and then for your partner to leave the UK once married and submit the application from her home country. Presumably you consider this not practical and that your child’s welfare might suffer if your partner were forced to leave for a period of time.For this reason you should instruct a solicitor in order to ultimately prepare and spouse visa application once you are married.
The webpage on spouse visas is here:https://www.gov.uk/join-family-in-uk
The eligibility criteria is here:-https://www.gov.uk/uk-family-visa/partner-spouse
Your solicitor will put you in the best position possible given your circumstances. Ultimately you will probably have to appeal and it will take a considerable time in order to appeal but your partner/wife will likely be successful in obtaining leave to remain on this basis but only if you instruct a solicitor.
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