I just want to know if any verse in the Quran mentions that Shaithan came with Adam to Earth from Paradise.
There are a couple of verses which can be used as an evidence for the exodus from Paradise, for example you may read it in surat al-Baqara in the verse, but you should read it in context to the verses before:
But Satan caused them to slip out of it and removed them from that [condition] in which they had been. And We said, "Go down, [all of you], as enemies to one another, and you will have upon the earth a place of settlement and provision for a time." (2:36)
This verse shows that earth will be their destination and place of stay for the rest of their lives. And later in the same surah Allah () says:
We said, "Go down from it, all of you. And when guidance comes to you from Me, whoever follows My guidance - there will be no fear concerning them, nor will they grieve. (2:38)
in surat al-'Araaf again earth is mentioned as the destination for settlement:
[ Allah ] said, "Descend, being to one another enemies. And for you on the earth is a place of settlement and enjoyment for a time." (7:24)
and in surat Taha:
[ Allah ] said, "Descend from Paradise - all, [your descendants] being enemies to one another. And if there should come to you guidance from Me - then whoever follows My guidance will neither go astray [in the world] nor suffer [in the Hereafter]. (20:123)
all these verses must be read in context.