We compute the Kauffman bracket skein module of the complement of a twist knot, finding that it is free and infinite dimensional. The basis consists of cables of a two-component link, one component of which is a meridian of the knot. The cabling of the meridian can be arbitrarily large while the cabling of the other component is limited to the number of twists.
"The Kauffman bracket skein module of a twist knot exterior." Algebr. Geom. Topol. 5 (1) 107 - 118, 2005. https://doi.org/10.2140/agt.2005.5.107