Εν is use by Jesus as ‘in the power of’. Although there is no explicit mention of power/ability, the verb εκβαλλω and the context of demon possession makes this sense fit. The idea is not so much power/authority as one of agency (see below).
See BDAG sv εν 6 agency.
Wallace has discussion of whether εν + dative can express personal agency or simply means/instrument. In this context of driving out demons this issue is heightened because it relates to who has authority over whom. Is Jesus the subject using Beelzebub as an agent or vice versa. Perhaps this is why Jesus reacts so harshly with talk of the ‘unforgivable sin’.
Closely related passage: Matt 9:34