Well, there are influencers out there that say that the best time of day to post on LinkedIn is 8:30 a.m. Eastern time to 9:30 a.m. Eastern time and that's if you're targeting CEOs and executives. If you're targeting people that are more marketing managers or more mid-level managers, I would say during lunchtime.
I say the best time to post on LinkedIn is whenever you can. Post whenever you're looking at LinkedIn. If you're on LinkedIn, post. Just do it whenever, I don't care if it's 3 a.m. on Sunday, post.