The bulk of Maxwell’s papers are housed at Cambridge University Library and elsewhere, but Trinity College Library does have some of his papers, as follows:
Miscellaneous papers, with artwork, designs for colour tops, and other geometric designs, a photograph of Maxwell as a young man holding a colour top, as well as a letter to his cousin Lizzie Cay about preparations for his wedding. Add. MS b. 52
Another group of miscellaneous papers with artwork, newscuttings, and a photograph of his wife Katherine and dog [Toby?]. Add.MS c/78
Fifteen letters to his friend Richard Buckley Litchfield dated 1853-1858, which include three letters not published in Harman’s Scientific Letters and Papers of James Clerk Maxwell. Add. MS c. 1/78-91
Four more letters in other collections: to Sir William Thomson, Add. MS a. 666/2, to Frederick Pollock, CLIF A7/1, to an unidentified recipient believed to be H. A. J. Munro, Add. MS c. 111/10, and to Arthur Cayley (not yet catalogued, in Adv. Album 3). The first two of these are not published in Harman’s Scientific Letters and Papers of James Clerk Maxwell.
A poem written by Maxwell, "Valedictory address to the Dean" on John Alexander Frere's retirement may be found in the Trinity College stories collected by J. McT. E. McTaggart, Add. MS c. 183-186.
A piece of knitting done by Maxwell for his aunt Mrs Isabella Wedderburn when he was a child. It is not yet catalogued, but has been photographed and described in the library blog, Mrs Wedderburn's Abigail.
Related papers include letters from James David Forbes to William Whewell about Maxwell early in his career, in Add. MS a. 204, and the notebook of one of his students, A. R. Forsyth, Add. MS a/189/3-6.