Owing to the characteristics of high density and unlimited write cycles, skyrmion racetrack memory (SK-RM) has demonstrated great potential as either the next-generation main memory or the last-level cache of processors with non-volatility. Nevertheless, the distinct skyrmion manipulations, such as injecting and shifting, demand a fundamental change in widely-used memory structures to avoid excessive energy and performance overhead. For instance, while Bε-trees yield an excellent query and insert performance trade-off between B-trees and Log-Structured Merge (LSM)-trees, the applicability of deploying Bε-trees onto SK-RM receives much less attention. In addition, even though optimizing designs have been proposed for B+-trees on SK-RM, those designs are not directly applicable to Bε-trees owing to the batch update behaviors between tree nodes of Bε-trees. Such an observation motivates us to propose the concept of Skyε-tree to effectively utilize the access port parallelism of SK-RM to embrace the excellent query and insert performance of Bε-trees. Experimental results have shown promising improvements in access performance and energy conservation.