You are welcomed anytime or You are welcomed at anytime?

不加atオ是正確的。
因anytime是副詞，是at any time 的意思，不是名詞，副詞直接修飾前面的動作，非名詞，前不可加at.

Anytime,tomorrow,the day before yesterday 等均是時間名詞而當副詞用，所以就不用畫蛇添足在其前面加介詞如本句at anytime，這在英文是習慣用法，其他類似的時間名詞均是如此使用

You are welcomed anytime(=adverb, also anyway:-used in spite of that; in any case)

You are most welcome.
You are welcome to visit our home anytime.

You are welcomed to our home anytime. (We welcome you to our home anytime.) 
You are always welcomed to our home.  (We always welcome you to our home.)

You are welcome anytime

較口語的說法，就直接說 ＂anytime＂了．

You are welcomed anytime.

不用at

You are welcomed anytime.

rusmannn jaimes 滾出台灣

應該是 You are welcomed anytime 我從來沒有看過anytime 前面需要+東西的