What roots does the word 'paradice' have, and why has it been changed to 'paradise' and since when?

Paradise was sometimes spelled with a C in Middle English, though it usually was spelled with S:

I wold not be in a folis paradyce. (Paston, 1462)

The S spelling was favored probably because of the etymology: both of its predecessors, Old French paradis and Latin paradīsus, are spelled with an S.

The time frame makes the reasoning behind the spelling pretty simple: spelling in Middle English wasn’t standardized, and the letters S and C both represent the same sound and were interchanged in many Middle English words. (It’s easy to find examples.) Looking at another word, spice, what is a C in Modern English could be a C, S, or even SC in the word in Middle English.

(Spice is also a word showing that the letters weren’t completely interchangeable. Cp- was not a valid onset spelling even in Middle English so you don’t find it ever spelled cpice or similar.)

Derivation

If you want to know the derivation of a word, etymonline.com is an excellent source.

paradise (n.)

late Old English, "the garden of Eden," from Old French paradis "paradise, garden of Eden" (11c.), from Late Latin paradisus "a park, an orchard; the garden of Eden

https://www.etymonline.com/search?q=paradise

Spelling

As far as I can tell, "paradice" was briefly an alternative spelling around the 1600s when English was undergoing a lot of change. Also, at that time there was no universal agreement on spelling.

Google nGram: paradice,paradise

Google nGram: paradice,paradise

You may be interested in researching further into the history of English spelling

History of English spelling

Printing adds to the muddle

William Caxton first set up in business as a printer in Bruges (now in Belgium). There in 1473 he made the first printed book in English, the Recuyell of the Historyes of Troye. Caxton returned to England in 1476 and set up a press in Westminster. The first book known to have been printed there was Chaucer's Canterbury Tales.

Caxton's spelling was based on the Chancery Standard, to which he added his own variants. Sadly, though printing brought many advantages, it also added to the irregularity of the spelling system. The printers Caxton brought with him from the Low Countries were unused to the English language and made spelling errors, eg any, busy, citie for eny, bisy, cittie.
...

The early dictionary writers

By the end of the 16th century, the uncertain and variable state of English spelling led to calls for its control. The first person to write a book of correct spelling in Early Modern English was Richard Mulcaster, first headmaster of Merchant Taylors' School, and later High Master of St Paul's School, both in London, who published The first Part of the Elementarie in 1582. The English Spelling Society