In order to claim the child tax credit, you must file an "on time" return that includes the child's social security number.
For 2019, it is too late to file an on time return, even if you had the extension, so for 2019 you can't claim the credit, even if you filed an amended return.
For 2020, a stepchild is treated for tax purposes exactly like a biological child, and you follow all the usual rules for claiming a dependent. (The child must be under 19, or under 24 and a student, must live in your home more than half the year, and can't provide more than half their own support.)
