Jennifer Pedranti's son and his friends apparently caused thousands of dollars in property damage with the fire Jennifer says they started in California ... TMZ has learned.

According to the Orange County Fire Authority Incident Information Fact Sheet obtained by TMZ, the brush fire near Ladera Ranch burned 7.70 acres and caused an estimated $10,000 in property damage.

The Orange County Fire Authority tells TMZ ... the investigation remains an open case ... and more information will be released once it has concluded.

As know ... "The Real Housewives of Orange County" star admitted on social media that her son was involved in starting the fire, apologizing to her neighbors and promising there would be consequences for her child.

A rep for the Orange County Fire Authority later told us ... "Three minors were interviewed as part of the investigation."

No one was injured or arrested in the incident, and the kids involved got a stern talking-to and were required to enroll in fire safety courses.

It's unclear if the alleged fire starters or their families will be required to compensate the city or county for the damage.