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We investigate excitonic transitions in a h-BN encapsulated monolayer $\textrm{MoS}_2$ phototransistor by photocurrent spectroscopy at cryogenic temperature (T = 5 K). The spectra presents excitonic peaks with linewidths as low as 8 meV, one order of magnitude lower than in earlier photocurrent spectroscopy measurements. We observe four spectral features corresponding to the ground states of neutral excitons ($\textrm{X}_{\textrm{1s}}^\textrm{A}$ and $\textrm{X}_{\textrm{1s}}^\textrm{B}$) and charged trions ($\textrm{T}^\textrm{A}$ and $\textrm{T}^\textrm{B}$) as well as up to eight additional spectral lines at energies above the $\textrm{X}_{\textrm{1s}}^\textrm{B}$ transition, which we attribute to the Rydberg series of excited states of $\textrm{X}^\textrm{A}$ and $\textrm{X}^\textrm{B}$. The relative intensities of the different spectral features can be tuned by the applied gate and drain-source voltages, with trions and Rydberg excited states becoming more prominent at large gate voltages. Using an effective-mass theory for excitons in two-dimensional transition-metal dichalcogenides we are able to accurately fit the measured spectral lines and unambiguously associate them with their corresponding Rydberg states. The fit also allows us to determine the quasiparticle bandgap and spin-orbit splitting of monolayer $\textrm{MoS}_2$, as well as the exciton binding energies of $\textrm{X}^\textrm{A}$ and $\textrm{X}^\textrm{B}$.