Is there any controller in stm32 series which has flash program size more than 2MB.

[S.Ma]

Not yet?

STM32 with cache manage pretty well performance wise with QSPI or OctoSPI external serial memory extension. STM32H series.

[Tesla DeLorean]

Might want to ponder the appropriateness of application/task

Several of the L4, F7 and H7 parts support Execute-In-Place via QSPI

Some of the F4/F7 can use SDRAM and NOR, the former could have code packed in NAND

Generally the CM7 parts are recommended as caching is architected into the core

[Tesla DeLorean]

https://community.st.com/s/question/0D50X0000AqtZBPSQ2/stm32f429ig-is-able-to-burn-code-with-17-mb-program-size-indicated-by-keil

The HY-STM32F429IG has NAND and SDRAM, code could be saved into NAND and copied into SDRAM to be run, but execution will be slow, so you'll want to balance where you place critical code.

Rather than in-line screen shots of the web page, just link to it direct;y

https://www.hotmcu.com/hystm32f429ig-development-board-with-independent-lcd-modules-p-263.html