Intermediate layers (ILs) are regions of enhanced electron density located in the ionospheric valley that extends from the peak altitude of the daytime E-region to the bottom side of the F-region. This work presents the daytime behavior of the ILs parameters (the virtual height - h’IL, and the top frequency - ftIL) for the deepest solar minimum of the last 500 years. In such a unique condition, this research reveals for the first time the ILs' quiet state seasonal behavior as well as its responses to moderate changes in the geomagnetic activity. Among the finds, it is highlight the annual periodicity of the ftIL while the h’IL presents semiannual component. The results also show that even small variations of geomagnetic activity (quantified by the planetary Kp index) are able to modify the dynamics of the ILs parameters. For the first time, it was observed that during December solstice and September equinox, the h’IL/ftIL decrease/increase rapidly with the increase of geomagnetic activity at the beginning of the day. As the day progresses, smoothed rise in the h’IL is observed at the same time in which a considerable decrease in the ftIL occurs, except during June solstice when a different behavior is observed both in relation to the annual as the seasonal average values of the ftIL.