"Keep hearing random rumors of me & Brandon splitting or that's he's cheating on me. Stop with all the lying please #aintnobodygottimeforthat," she wrote.
The former American Idol star added, "False rumors don't bother me & Brandon but they do affect the lives of our 12 & 7 yr old.They're kids &don't get that people can print lies."
Blackstock responded to the allegations via Twitter as well.
When one fan wrote, "It's sad how low life's make up rumors about @BBlackstock," he responded, "But it makes for great reading while on the s--tter."
Meanwhile, Blackstock's ex-wife attested to his good character and said that the cheating rumors were "silliness."Melissa Ashworth claimed that Blackstock is an excellent parent and was faithful to her during their marriage.
"This is ridiculous," she told Radar. "I have my two children [by Brandon] right here, who I love."
She added, "I adore Kelly and Brandon has a couple, so if I say anything it's going to be positive."
Clarkson announced that she was expecting the couple's first child in early November.
The two tied the knot at Blackberry Farm in Walland, Tenn., on Sunday, Oct. 20 in front of close friends and family.
The newlyweds met through the groom's dad, Narvel Blackstock, who has been Clarkson's manager for years and is married to her onetime touring partner Reba McEntire.
