Can I claim a child that I have custody of while his parent is incarcerated, his mother is deceased?

Are you a blood relative or is the child with you in foster care?  Also, how long was the child with you?

He is my cousin and I have had him in my custody since june 2016

If the child meets the following qualifications, he/she may be your dependent:

The bottom line is a dependent must be your “qualifying child” or “qualifying relative” and meet specific tests in order for you to claim them.

The 5 tests that will qualify a child as a dependent are:

• Relationship: Must be your child, adopted child, foster-child, brother or sister, or a descendant of one of these (grand or nephew).
• Residence: Must have the same residence for more than half the year.
• Age: Must be under age 19 or under 24 and a full-time student for at least 5 months. They can be any age if they are totally and permanently disabled.
• Support: Must not have provided more than half of their own support during the year.
• Joint Support: The child cannot file a joint return for the year.

The 4 tests that will qualify a relative as a dependent are:

• Qualifying Child: They are not the “qualifying child” of another taxpayer or your “qualifying child”.
• Gross Income: The dependent being claimed earns less than $4,050 in 2017 ($4,050 in 2016).
• Total Support: You provide more than half of the total support for the year.
• Member of Household or Relationship: The person (a friend, girlfriend, non-blood relative) must live with you all year as a member of your household.

https://blog.turbotax.intuit.com/tax-deductions-and-credits-2/family/who-can-i-claim-as-a-dependent-...