Step 1: Identify the party.
AITC stands for {All India Trinamool Congress}, a national party with its stronghold in West Bengal.
Step 2: Founding episode.
Mamata Banerjee founded AITC in 1998 after splitting from the Indian National Congress, positioning it as a regional challenger to the CPI(M) in Bengal and later as a national player.
Step 3: Verify against distractors.
Jyoti Basu was a veteran {CPI(M)} leader and long-time Chief Minister; Sharad Pawar founded the {NCP}; J. Jayalalitha led the {AIADMK}. None of these are related to AITC's establishment.
Step 4: Conclude.
\[
\boxed{\text{Mamata Banerjee (Option B) is the founder of AITC (1998).}}
\]