© 2018, © 2018 Taylor & Francis.In the Khovanov homology of links, presence of (Formula presented.) -torsion is a very common phenomenon. Finite number of examples of knots with (Formula presented.) -torsion for n > 2 were also known, none for n > 8. In this article, we present several infinite families of links whose Khovanov homology contains (Formula presented.) -torsion for 2 < n < 9 and (Formula presented.) -torsion for s < 24. We introduce 4-braid links with (Formula presented.) -torsion which are counterexamples to parts of the PS braid conjecture. We also provide an infinite family of knots with (Formula presented.) -torsion in reduced Khovanov homology and (Formula presented.) -torsion in odd Khovanov homology.