Your fiance will likely qualify to file as Head of Household, as he maintained a home for his child for the entire year. He must have paid more than half the cost of maintaining the home in 2018 and be unmarried. More information of filing as Head of Household can be found here: Filing as Head of Household He will claim his child as a dependent, unless he has an agreement with the child's mother allowing her to claim the child.
While it is possible to claim a non-relative as a dependent under the qualifying relative rules, certain requirements must be met. In your situation, he cannot claim you as a dependent in 2018 because your income exceeded the $4,150 limit for claiming a non-relative. If you are required to file, you will file as Single. Your child's situation will depend if you are required to file, the filing situation of the child's father, and any agreement you have with the father. If your son is not the qualifying child of you or his father (per tax rules), it may be possible for your fiance to claim him. See more here: Rules for Claiming a Dependent
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