We present redshift-space two-point ({xi}), three-point ({dzeta}), and reduced three- point (Q) correlation of Ly{alpha} absorbers (Voigt profile components having HI column density, N_HI_>10^13.5^cm^-2^) over three redshift bins spanning 1.7<z<3.5 using high-resolution spectra of 292 quasars. We detect positive {xi} up to 8h^-1^cMpc in all three redshift bins. The strongest detection of {dzeta}=1.81+/-0.59 (with Q=0.68+/-0.23) is in z=1.7-2.3 bin at 1-2h^-1^cMpc. The measured {xi} and {dzeta} values show an increasing trend with N_HI_, while Q remains relatively independent of N_HI_. We find {xi} and {dzeta} to evolve strongly with redshift. Using simulations, we find that {xi} and {dzeta} seen in real space may be strongly amplified by peculiar velocities in redshift space. Simulations suggest that while feedback, thermal and pressure smoothing effects influence the clustering of Ly{alpha} absorbers at small scales, i.e. <0.5h^-1^cMpc, the HI photoionization rate ({GAMMA}_HI_) has a strong influence at all scales. The strong redshift evolution of {xi} and {dzeta} (for a fixed N_HI_ cut-off) is driven by the redshift evolution of the relationship between _HI_ and baryon overdensity. Our simulation using best- fitting {GAMMA}_HI_(z) measurements produces consistent clustering signals with observations at z~2 but underpredicts the clustering at higher redshifts. One possible remedy is to have higher values of {GAMMA}_HI_ at higher redshifts. Alternatively the discrepancy could be related to non-equilibrium and inhomogeneous conditions prevailing during He ii reionization not captured by our simulations.