High-precision time synchronization is a vital prerequisite for many modern applications and technologies, including Smart Grids, Time-Sensitive Networking (TSN), and 5G networks. Although the Precision Time Protocol (PTP) can accomplish this requirement in trusted environments, it becomes unreliable in the presence of specific cyber attacks. Mainly, time delay attacks pose the highest threat to the protocol, enabling attackers to diverge targeted clocks undetected. With the increasing danger of cyber attacks, especially against critical infrastructure, there is a great demand for effective countermeasures to secure both time synchronization and the applications that depend on it. However, current solutions are not sufficiently capable of mitigating sophisticated delay attacks. For example, they lack proper integration into the PTP protocol, scalability, or sound evaluation with the required microsecond-level accuracy. This work proposes an approach to detect and counteract delay attacks against PTP based on cyclic path asymmetry measurements over redundant paths. For that, we provide a method to find redundant paths in arbitrary networks and show how this redundancy can be exploited to reveal and mitigate undesirable asymmetries on the synchronization path that cause the malicious clock divergence. Furthermore, we propose PTPsec, a secure PTP protocol and its implementation based on the latest IEEE 1588-2019 standard. With PTPsec, we advance the conventional PTP to support reliable delay attack detection and mitigation. We validate our approach on a hardware testbed, which includes an attacker capable of performing static and incremental delay attacks at a microsecond precision. Our experimental results show that all attack scenarios can be reliably detected and mitigated with minimal detection time.