Physics of quantum critical point is one of the most perplexing topics in current condensed-matter physics. Its conclusive understanding is forestalled by the scarcity of experimental systems displaying novel aspects of quantum criticality. We present a comprehensive experimental evidence of a magnetic field tuned tricritical point separating paramagnetic, antiferromagnetic and metamagnetic phases in novel CePtIn4. Analyzing field variations of its magnetic susceptibility, magnetoresistance and specific heat at very low temperatures we trace modifications of antiferromagnetic structure of the compound. Upon applying magnetic field of increasing strength, the system undergoes metamagnetic transitions which persist down to the lowest temperature investigated, exhibiting first-order-like boundaries separating magnetic phases. This yields a unique phase diagram where the second-order phase transition line terminates at a tricritical point followed by two first-order lines reaching quantum critical end points as T 0. Our findings demonstrate that CePtIn4 provides innovative perspective for studies of quantum criticality.