The shooting happened around 1 a.m. Sunday in the 5000 block of Roth Forest Lane in Spring.
According to the sheriff, shots were fired at the home from a suspect, striking both the mother and her 11-year-old son.
Gonzalez says the shooting happened after an argument between juveniles at a separate residence.
The 11-year-old left the residence and was followed by other people trying to instigate a fight, Gonzalez says.
A parent de-escalated the situation temporarily. Later on, an older relative to one of the juveniles is said to have been involved in the drive-by shooting, according to deputies.
Gonzalez says the mother is in fair condition, but her son is in serious condition.
A suspect has been taken into custody. No other injuries were reported.