This week a judge granted Kardashian's request to restore her single status and she's once again using her maiden name.
West recently declared he wants "payback" and continues to take aim at Davidson, 28, on social media, but has insisted he's not harassing the star.
He recently posted a throwback snap of the comedian joking about his mental health struggles on Saturday Night Live. In the image, Davidson is seen wearing a cap that reads, "Make Kanye 2006 Again".
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The skit also made fun of West's friendship with former US President Donald Trump.
West - who refers to Davidson as "Skete" - wrote on Instagram: "HI SKETE YOU GOT ANYMORE MENTAL HEALTH JOKES FOR ME? (sic)".
He wrote: "This boy thought he could get away with performing this sketch for the team that wrote this for him."
However, he insisted "This is not harassment This is payback. (sic)"
In the skit, Davidson performed an impression of the rap star. The comedian said: "This is the real me. I am off the meds, take 'em, no shame in the medicine game."
West - who has previously been diagnosed with bipolar disorder - recently apologised for "harassing" Kardashian on social media.
West deleted all of his recent posts about his estranged wife and said he was "learning in real time".
Alongside a photo of himself on stage, West - who married Kardashian in 2014 - wrote: "I've learned that using all caps makes people feel like I'm screaming at them.
"I'm working on my communication. I can benefit from a team of creative
professionals, organisers, mobilizers and community leaders. Thank everybody for supporting me. (sic)"