In the quasi-one-dimensional heavy-fermion system YbNi4(P1-xAsx)(2) the presence of a ferromagnetic (FM) quantum critical point (QCP) at x(c) approximate to 0.1 with unconventional quantum critical exponents in the thermodynamic properties has been recently reported. Here, we present muon-spin relaxation (mu SR) experiments on polycrystals of this series to study the magnetic order and the low-energy 4f -electronic spin dynamics across the FM QCP. The zero-field mu SR measurements on pure YbNi4P2 proved static long-range magnetic order and suggested a strongly reduced ordered Yb moment of about 0.04 mu(B). With increasing As substitution, the ordered moment is reduced by half at x = 0.04 and to less than 0.005 mu(B) at x = 0.08. The dynamic behavior in the mu SR response shows that magnetism remains homogeneous upon As substitution, without evidence of a disorder effect. In the paramagnetic state across the FM QCP the dynamic muon-spin relaxation rate follows 1/T1T proportional to T-n with 1.01 +/- 0.04