In this paper we study the effect of a uniform magnetic field B-y in the cross-tail y direction on the dynamics and distribution function of energetic ions in a current sheet model including a neutral line. Martin and Speiser (1988) have previously shown that a ''ridge'' in the velocity space distribution function is a remote neutral line signature in a two-dimensional field without B-y. Our results show that as B-y is increased, using nominal tail parameters, there is very little change in the ridge signature for small B-y (up to about 4 times B-z). For intermediate values (up to about 10 times B-z) the ridge becomes observable further from the neutral line, while close to the X line the ridge is strongly modified. For large B-y (of the order of B-x) the ridge evolves into new neutral line signatures which depend strongly on whether the observation point is above or below the current sheet. These results are used to estimate B-y < 2 nT in the AMPTE/IRM event modeled by Speiser and Martin (1994), which is consistent with onboard magnetometer measurements. We further show that the cause of the new structures appearing at large B-y is the same source separation effect that produced the original ridge and that all these signatures ate relatively insensitive to a small parallel electric field. Finally, we point out a dynamical ordering which occurs at large B-y: Using high-resolution simulations, we find a common boundary separating regions of positive and negative initial x, y, and z position, as well as initial pitch angle. This boundary is purely dynamical in nature and is independent of modeled source distributions.