Yes, you can claim your grandchild, if he is under 19.
The non custodial parent, and his child support, is not relevant. The fact that his income is higher than yours is only relevant if he also lived with the child more than half the year.
________________________________________________________________________________________________________
There are two types of dependents,
"Qualifying Children"(QC) and standard ("Qualifying
Relative" in IRS parlance even though they don't have to actually be
related). There is no income limit for a QC but there is an age limit, a
relationship test and residence test. Only a QC qualifies a taxpayer for the
Earned Income Credit and the Child Tax Credit. They are interrelated but the
rules are different for each.
.A child closely related (grandchild counts) to a taxpayer can be a
“Qualifying Child (QC)” dependent, regardless of the child's income, if:
1.
He is under age 19, or under 24 if a full time
student for at least 5 months of the year, or
is totally & permanently disabled
2.
He did not provide more than 1/2 his own
support
3.
He lived with the relative (including temporary
absences) for more than half the year
4.
He is younger than the relative (not applicable
for a disabled child)
5.
If the
child meets the rules to be a qualifying child of more than one person, you
must be the person entitled to claim the child as a qualifying child (this
essentially means that you have the custodial parent’s permission to claim the child, if the child also lived with the
parent more than half the year). Note: the non custodial parent is irrelevant
6.
If the parents of a
child can claim the child as a qualifying child but no parent so claims the
child, no one else can claim the child as a qualifying child unless that
person's adjusted gross income (AGI) is higher than the highest AGI of any of
the child's parents who can claim the child. Note: the non custodial parent is irrelevant. This rule applies only to the mother (custodial parent) of the child
https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
