Hogg dedicated Pilgrims of the Sun (1815) to Byron.
Hogg wrote poetic parodies of major poets (including Wordsworth, Coleridge, Byron, Scott, Wilson, Southey, and himself) in The Poetic Mirror (1816) (ODNB; Murray, The Works of Lord Byron vol. 10 (1904), p. 116); Hogg's poem on Byron is "The 'Guerilla,' " which subverts the typically aristocratic Byronic hero by presenting the protagonist as a peasant.
"Among the Byron papers are preserved some letters from Hogg ... Byron's letters to Hogg, which the Shepherd carefully treasured, were, it appears (Memorials of James Hogg, p. 188), stolen by a visitor" (Murray, The Works of Lord Byron vol. 10 (1904), p. 116).