The other attorney answers are on target. The only issue may be for your wife if you filed the petition for her residency based upon the marriage. The length of time the two of you were married is important, although the fact that you and she presumably had a child together should defeat any idea of there have been fraud in the marriage for purposes of establishing residency.
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The divorce process is not necessarily altered in any significant way as a result of your wife's immigration status. As long as you have been a resident of New Jersey for the past year and your wife has similar ties to New Jersey, New Jersey will have jurisdiction to address your divorce matter.
Issues of setting alimony and child support require more facts and information than you have provided, although if your annual income is truly only $27,000 a year your exposure to having a significant alimony obligation will surely be minimal.
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I agree with the prior response. You appear to have jurisdiction in New Jersey and there is not enough info for us to know amounts for child support or alimony. There are many factors that go into these financial calculations and alimony is particularly tricky since it is not an exact formula. There may also be an immigration issue if you are indicating that your wife is not a permanent resident, because many times folks her illegally apply for their permanent residence through their marriage. Clearly, if you are divorcing, she can no longer use or rely upon you to become legal. If you can find a decent divorce lawyer in your area who also handles immigration issues, that may be your best bet. Best of luck to you.
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