Mixed models can variable be both fixed and random

#1
I am conducting an analysis over multiple subjects over several sessions with two types of controls.

I want to conduct a mixed model analysis to see if there is a difference with respect to control type.

This is what i have so far:
I have session nested in subject.
Accuracy= dependent variable
Fixed variables: Controltype (Type) and sessions (Sess)
Random Variables: slope and intercept of session over time with respect to each subject

This is the R code I am using
Accuracy.model = lmer(Accuracy ~ Sess + Type + (1+Sess|ID), data=AccuracyMtVsSg , REML=FALSE)
Accuracy.null = lmer(Accuracy ~ Sess + (1+Sess|ID), data=AccuracyMtVsSg , REML=FALSE)
anova(Accuracy.null,Accuracy.model)


I am interested in whether Type effects accuracy.....

Am I correct to include session as a fixed effect (since there could be changes over time that are similar among all subjects) and random effect ?

Thanks for the help!!!