  Semiconductor quantum dots (QDs) enable the generation of single and
entangled photons, useful for various applications in photonic quantum
technologies. Specifically for quantum communication via fiber-optical
networks, operation in the telecom C-band centered around 1550$\,$nm is ideal.
The direct generation of QD-photons in this spectral range and with high
quantum-optical quality, however, remained challenging. Here, we demonstrate
the coherent on-demand generation of indistinguishable photons in the telecom
C-band from single QD devices consisting of InAs/InP QD-mesa structures
heterogeneously integrated with a metallic reflector on a silicon wafer. Using
pulsed two-photon resonant excitation of the biexciton-exciton radiative
cascade, we observe Rabi rotations up to pulse areas of $4\pi$ and a high
single-photon purity in terms of $g^{(2)}(0)=0.005(1)$ and $0.015(1)$ for
exciton and biexciton photons, respectively. Applying two independent
experimental methods, based on fitting Rabi rotations in the emission intensity
and performing photon cross-correlation measurements, we consistently obtain
preparation fidelities at the $\pi$-pulse exceeding 80$\%$. Finally, performing
Hong-Ou-Mandel-type two-photon interference experiments we obtain a
photon-indistinguishability of the full photon wave packet of up to $35(3)\%$,
representing a significant advancement in the photon-indistinguishability of
single photons emitted directly in the telecom C-band.
