A search for supersymmetric partners of top quarks decaying as (t) over tilde (1) -> c (chi) over tilde (0)(1)and supersymmetric partners of charm quarks decaying as (c) over tilde (1) -> c (chi) over tilde (0)(1) where (chi) over tilde (0)(1) is the lightest neutralino, is presented. The search uses 36.1 fb(-1) pp collision data at a centre-of-mass energy of 13 TeV collected by the ATLAS experiment at the Large Hadron Collider and is performed in final states with jets identified as containing charm hadrons. Assuming a 100\% branching ratio to c (chi) over tilde (0)(1), top and charm squarks with masses up to 850 GeV are excluded at 95\% confidence level for a massless lightest neutralino. For m (t) over tilde (1,(c) over tilde1) - m((chi) over tilde 10)< 100 GeV, top and charm squark masses up to 500 GeV are excluded.