Short answer: There is no doctrinal connection. In Jain Dharma, the only supreme ideals are Arihant, Siddha, Sadhu, and Shastra. “Shivji” as worshipped in the Hindu tradition is not a Tirthankar or supreme being in Jainism.

Helpful clarity from the Jain view:

• Meaning of “Shiv”: In many Jain texts “shiv/śiva” means auspicious, peace, or the bliss of liberation (moksha). It is an adjective for the state of the Siddhas, not the name of a deity.
• 24 Tirthankars are distinct: For example, Bhagwan Rishabhdev (Adinath) is sometimes culturally confused with “Shiva” due to matted hair or the bull symbol, but in Jain siddhant he is a Tirthankar, not Shiva.
• Devas, Yakshas, Kshetrapal: Jains acknowledge many celestial beings (dev, yaksha‑yakshini, kshetrapal) as samsari souls who can be helpful protectors. Some of these are locally identified with names familiar in Shaiva traditions (like Bhairav as a kshetrapal), but they remain worldly beings, never supreme or liberators in Jainism. Ultimate refuge is only in the Tirthankars and the path they reveal.

Bottom line:

• The connection is cultural and linguistic in some regions, not theological.
• Jain worship and liberation-path remain independent: Right Faith, Right Knowledge, Right Conduct, with reverence to Arihant–Siddha–Sadhu–Shastra.