Results from some recent numerical works, including ours, lend credence to the thesis that the ambient environment, that is, the magnitude of external pressure, affects the star-forming ability of clouds and filaments. In continuation with our series of papers on this subject, we explore this thesis further by developing new hydrodynamic simulations of accreting filaments confined by external pressures in the range $10^{4 -7}$ K cm$^{-3}$. Our principal findings are – (i) irrespective of linemass, filament-fragmentation generally yields spheroidal cores. The initially sub-critical filaments in low to intermediate external pressure environments form broad cores suggesting that weakly self-gravitating filaments must fragment via the collect – and- collapse mode to form broad cores. Transcritical filaments, by contrast, become susceptible to the Jeans-type instability and form pinched cores; (ii) the ambient environment bears upon the physical properties of filaments including their FWHM$_{fil}$. Only the filaments initially suffused with subsonic turbulence in Solar-Neighbourhood-like environments, however, have FWHM$_{fil}$$\sim$ 0.1 pc. In high pressure environs such filaments not only have much smaller widths, but also become severely eviscerated. On the contrary, filaments suffused with initially supersonic turbulence are typically broader; (iii) the quasi-oscillatory nature of velocity gradients must be ubiquitous along filament lengths and its magnitude generally increases with increasing pressure. The periodicity of the velocity gradients approximately matches the fragmentation lengthscale of filaments; (iv) oscillatory features of the radial component of the velocity gradient are a unreliable proxy for detecting signatures of accretion onto filaments; and (v) filaments at either extreme of external pressure are inefficient at cycling gas into the dense phase which could reconcile the corresponding inefficiency of star-formation in such environments.