Since current widely available network protocols/systems are mainly throughput-oriented designs, meeting stringent delay requirements of new applications such as virtual reality and vehicle-to-vehicle communications on cellular network requires new network protocol/system designs. C2TCP is an effort toward that new design direction. C2TCP is inspired by in-network active queue management (AQM) designs such as RED and CoDel and motivated by lack of a flexible end-to-end (e2e) approach which can adapt itself to different applications' QoS requirements without modifying any network devices. It copes with unique challenges in cellular networks for achieving ultra-low latency (including highly variable channels, deep per-user buffers, self-inflicted queuing delays, radio uplink/downlink scheduling delays) and intends to satisfy stringent delay requirements of different applications while maximizing the throughput. C2TCP works on top of classic throughput-oriented TCP and accommodates various target delays without requiring any channel prediction, network state profiling, or complicated rate adjustment mechanisms. We have evaluated C2TCP in both real-world environment and extensive trace-based emulations and compared its performance with different TCP variants and state-of-the-art schemes including PCC-Vivace, Google's BBR, Verus, Sprout, TCP Westwood, and Cubic. Results show that C2TCP outperforms all these schemes and achieves lower average delay, jitter, and 95th percentile delay for packets.