Sources familiar with the situation tell TMZ … all of Diddy’s kids are supportive of him and stand behind him, adding they love their dad and think he's a great father.

We're told all Diddy's sons and daughters have wonderful relationships with him and will continue to maintain those relationships ... even though he's in custody after being indicted on sex trafficking, kidnapping and racketeering charges.

Our sources say Diddy's twin daughters, 17-year-olds D'Lila and Jessie, are keeping their father in their daily prayers and remain hopeful he will be released from jail. We're told they haven't read the indictment and have no interest in doing so.

Diddy's older sons were with him at court last week, but the twins are hanging back in California, where we're told they have a great support team around them ... including Kimora Lee Simmons and their late mother Kim Porter's longtime friend, Lala.

Our sources say the twins view Lala and Kimora as mother figures and they are both doing their best to make sure the girls are not focused on Diddy's arrest ... instead making sure the girls are empowered and protected during this time.

Diddy's being held at the Metropolitan Detention Center in NYC and sources close to the family tell TMZ ... Diddy's mother and some of his kids have spoken to him by phone since he's been locked up.