  We consider the $p$-adic random walk model in a potential, which can be
viewed as a generalization of $p$-adic random walk models used for description
of protein conformational dynamics. This model is based on the
Kolmogorov--Feller equations for the distribution function defined on the field
of $p$-adic numbers in which the probability of transitions per unit time
depends on ultrametric distance between the transition points as well as on
function of potential violating the spatial homogeneity of a random process.
This equation, which will be called the equation of $p$-adic random walk in a
potential, is equivalent to the equation of $p$-adic random walk with modified
measure and reaction source. With a special choice of a power-law potential the
last equation is shown to have an exact analytic solution. We find the analytic
solution of the Cauchy problem for such equation with an initial condition,
whose support lies in the ring of integer $p$-adic numbers. We also examine the
asymptotic behaviour of the distribution function for large times. It is shown
that in the limit $t\rightarrow\infty$ the distribution function tends to the
equilibrium solution according to the law, which is bounded from above and
below by power laws with the same exponent. Our principal conclusion is that
the introduction of a potential in the ultrametric model of conformational
dynamics of protein conserves the power-law behaviour of relaxation curves for
large times.
