  In the Gaia era, the membership analysis and parameter determination of open
clusters (OCs) are more accurate. We performed a census of OC's classical
Cepheids based on Gaia Early Data Release 3 (EDR3) and obtained a sample of 33
OC Cepheids fulfilling the constraints of the spatial position, proper motion,
parallax and evolution state. 13 of 33 OC Cepheids are newly discovered. Among
them, CM Sct is the first first-crossing Cepheids with direct evidence of
evolution. DP Vel is likely a fourth- or fifth-crossing Cepheids. Based on
independent distances from OCs, W_1-band period-luminosity relation of Cepheids
is determined with a 3.5% accuracy: <MW1> = -(3.274 +- 0.090) log P - (-2.567
+- 0.080). The Gaia-band period-Wesenheit relation agrees well with Ripepi et
al. (2019). A direct period-age relation for fundamental Cepheids are also
determined based on OC's age, that is log t = -(0.638 +- 0.063) log P + (8.569
+- 0.057).
