If at all, it is not your ability to qualify for an Affidavit of Support that your criminal conviction will affect, but possibly your ability to petition for a foreign national spouse under the Walsh Act. But not if a misdemeanor. Take your conviction record for review by an immigration lawyer.
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PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
Your criminal record of domestic violence does not impact your ability to provide financial support for the beneficiary. If you have substantial income, you can provide affidavit of support for people who you don't live with which means your domestic violence propensities is not at issue