Quantitative timing is often explicitly used in systems for better security, e.g., the credentials for automatic website logon often has limited lifetime. Verifying timing relevant security protocols in these systems is very challenging as timing adds another dimension of complexity compared with the untimed protocol verification. In our previous work, we proposed an approach to check the correctness of the timed authentication in security protocols with fixed timing constraints. However, a more difficult question persists, i.e., given a particular protocol design, whether the protocol has security flaws in its design or it can be configured secure with proper parameter values? In this work, we answer this question by proposing a parameterized verification framework, where the quantitative parameters in the protocols can be intuitively specified as well as automatically analyzed. Given a security protocol, our verification algorithm either produces the secure constraints of the parameters, or constructs an attack that works for any parameter values. The correctness of our algorithm is formally proved. We implement our method into a tool called PTAuth and evaluate it with several security protocols. Using PTAuth, we have successfully found a timing attack in Kerberos V which is unreported before.