We present a search for a new particle T′ decaying to a top quark via T′→t+X, where X goes undetected. We use a data sample corresponding to 5.7  fb−1 of integrated luminosity of pp collisions with s√=1.96  TeV, collected at Fermilab Tevatron by the CDF II detector. Our search for pair production of T′ is focused on the hadronic decay channel, pp→T′T′→tt+XX→bqqbqq+XX. We interpret our results in terms of a model where T′ is an exotic fourth generation quark and X is a dark matter particle. The data are consistent with standard model expectations. We set a limit on the generic production of T′T′→tt+XX, excluding the fourth generation exotic quarks T′ at 95% confidence level up to mT′=400  GeV/c2 for mX≤70  GeV/c2.