Who should claim my son?

[Ebw900]

I have been a stay at home mom for 3 years. 
I have a legal agreement with my sons father for every other year. The first year I stayed home my fiancé claimed my me and my son on his taxes since he provided all. 
now, I opened up my own business 2019. 
this tax season is my year to claim my son. 
I do not pay for the mortgage, or utilities my fiancé does. 

So what do I do? 

[RayW7]

If the father will agree to signing Form 8832, this will solve the problem.

The Internal Revenue Service (IRS) allows you to potentially reduce your tax by claiming a dependent child on a tax return. If you do not file a joint return with your child's other parent, then only one of you can claim the child as a dependent. When both parents claim the child, the IRS will usually allow the claim for the parent that the child lived with the most during the year.

There is one exception to the residence requirement that allows the non-custodial parent to claim their child as a dependent. The non-custodial parent can claim the child as a dependent if the custodial parent agrees not to on their own tax return. However, you must obtain a signed IRS Form 8332 or similar written document from the custodial parent allowing you to do so. Parents who have joint custody may also use this form to alternate the tax years in which each can claim the dependent.

If  no agreement can be reached then the IRS will use the Tie Breaker Rules

• Tie Breaker Rules

[Mike9241]

the IRS says the custodial parent gets to claim but if you are claimed as a dependent on another's return you can't can any dependents.  since you are not married you can't file a joint return with your fiance.  you had your own business in 2019 and 2020. if your gross income from it (for schedule C net sales minus cost of sales) plus any other income was more than $4300 in 2020 (even less in 2019)  your fiance was not entitled to claim you or your child (you would not be his qualifying relative). a custodial parent has a higher priority in claiming their child than a nonrelative even if the nonrelative provides over 50% of the child's support.

the IRS doesn't care about what divorce decrees say as to whom may claim their child. we can't give legal advice as to what would happen if you (or your fiance) claimed the child in the year his father is entitled to under the divorce decree.  

as described above if your gross income was more than $4300 for 2020 you file as head of household and claim your son. (your income would disqualify him from claiming you as a qualifying relative (QR) and if he can't claim you as a QR he can't claim your child. Your fiance, unless he has other dependents that would also qualify him to file as head of household, would have to file as single.     

the issue is 2019, which is as stated above is a legal issue as to who was entitled per the decree to claim the child. It's only a tax issue if your fiance was not entitled to claim you and your son as dependents under the tax laws.  then your return would also be incorrect.