  A superspace approach to the Becchi-Rouet-Stora-Tyutin (BRST) formalism for
the Yang-Mills theory on an n-dimensional unit sphere, S_1^{n}, is developed in
a manifestly covariant manner based on the rotational supersymmetry
characterized by the supergroup OSp(n+1|2). This is done by employing an
(n+2)-dimensional unit supersphere, S_1^{n|2}, parametrized by n commutative
and 2 anticommutative coordinate variables so that it includes S_1^{n} as a
subspace and realizes the OSp(n+1|2) supersymmetry. In this superspace
formulation, referred to as the supersphere formulation, the so-called
horizontality condition is concisely expressed in terms of the rank-3 field
strength tensor of a Yang-Mills superfield on S_1^{n|2}. The supersphere
formulation completely covers the BRST gauge-fixing procedure for the
Yang-Mills theory on S_1^{n} provided by us [R. Banerjee and S. Deguchi, Phys.
Lett. B 632 (2006) 579, arXiv:hep-th/0509161]. Furthermore, this formulation
admits the (massive) Curci-Ferrari model defined on S_1^{n}, describing the
gauge-fixing and mass terms on S_1^{n} together as a mass term on S_1^{n|2}.
