f means density function what are Y and y
It's probably the partial derivative of f with respect to Y at y.
Or, in some cases, the capital Y can represent the restriction of the domain of f to Y.
with respect to probability(its not what you said)
[itex]f_Y[/itex] is the given density function of random variable Y and [itex]f_Y(y)[/itex] is its value for some specific value y.
Separate names with a comma.