tWitch's mother is concerned his widow Allison Holker is creating a stain on his legacy ... by claiming he had a drug problem.

Connie Boss Alexander takes issue with Allison and her new book in a new CBS interview with Gayle King ... voicing doubts about Allison's claims that tWitch was big into drugs.

tWitch's mom tells Gayle she's not doubting he experimented with substances now and then ... she just doesn't believe things rose to the scope Allison claims -- namely, a shoebox full of drugs.

Allison says she wrote a book about tWitch to raise awareness about mental health issues in the wake of his suicide ... but Connie says Allison should have handled things better.

The big issue ... tWitch's mother worries about the impact the drug claims will have on his children.

Gayle says the family rift really boils down to tWitch's family feeling like they don't get enough time with the kids he shared with Allison.

tWitch's mom ripped Allison on social media when the drug claims first surfaced, and now she's taking her beef to national TV.

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