Shiva Purana
यः प्रधानतया काश्या मध्ये तिष्ठति शङ्करः ॥ स्वपुरीजन सौख्यार्थमतोऽसौ मध्यमेश्वरः॥ ८०॥
Śiva is called Madhyameśvara since he is stationed mainly in the centre of Kāśī for bestowing happiness on the people.
english translation
yaH pradhAnatayA kAzyA madhye tiSThati zaGkaraH ॥ svapurIjana saukhyArthamato'sau madhyamezvaraH॥ 80॥
hk transliteration by Sanscript