Start with https://covidlegalusa.com/fighting-mandatory-vaccines/ and https://americasfrontlinedoctors.org/legal/. The frontline doctors have a form you can fill out to get in touch with an attorney.

Not to be overly critical, but the image in your post states that employees will be "asked" to submit verification. It says nothing about a requirement. Though it probably feels like a requirement, I work for a lawyer and I can tell you that on its face, there is no requirement being announced there and a court of law will determine the same (it's always about what you can prove). However, if you choose to pursue such a thing and wish to receive recommendations for lawyers, you need to say what state you live/work in because attorneys can only practice in the states in which they are admitted to the state bar association. In short, nobody will be able to recommend a lawyer if they don't know what state you live/work in. You may wish to visit the America's Frontline Doctors website. There might be info helpful to you there. I hope that helps.