Possibly. Who do the children live with and how old are they? Are you just living away for work temporarily or is this a permanent move on your part? Are you paying the bills or paying child support? If the children live with the other parent and you are not married, then the other parent may be able to claim them since they live with them more than 6 months out of the year.
Your children do not always have to live in the same house as you in order to claim them as a dependent. However, in a situation where someone would be paying child support that covers over half of the living expenses but the kids live with the other parent, the parent the kids live with would be the one to claim them under the Tie Breaker Rules.
If you are only temporarily away for work, then it would count the same as you living in the house if you were going back to the house when your job is complete.
You would not be eligible for all credits. For example, the EITC is only available if your child lived with you for more than half of the year.
If the child lives with the other parent, then you may be able to claim the Child Tax Credit, if the other parent agrees to it and you include form 8832 on your return. The non custodial parent can also claim the child and dependent care credit.
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