The Jedi cult had its up and downs. When were they the strongest? Was it somewhere in EP1-EP3?
Definition of strongest: most followers, most influence, most respect (, most power?)
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In Legends, Jedi were most powerful before the Ruusan Reformation during New Sith Wars. Jedi in that era were truly knights: powerful Force warriors that utilized armor and had their own armies, titles, and families. Some of them were actually Supreme Chancellors of the Republic like for example Genarra.
The Ruusan Reformation neutered the Jedi Order, forcing them to abandon their power (both political and in the Force), turning them into a monastic order and extinguishing powerful Force bloodlines. Jedi in the final years of the Republic were a mockery and pale shadow of the Jedi from the previous era, making them relatively a easy target for the reformed Sith.
In Canon, the situation is unclear but previous generations of Jedi had more Force power. All we know from the Canon is that in some point in the time there was a devastating war between the Jedi and the Sith. Jedi from this era had more knowledge then Jedi in the waning days of the Republic, and were even able to build time-traveling sites like the Jedi Temple on Lothal
Jedi from episodes 1-3 seemingly had great political power (generals of the Clone Army) but in reality their attachment to the corrupt Republic was a weakness which led to almost total destruction of their Order.
I cannot speak to their respect or influence, but their power seems to have peaked thousands of years before the prequels. A Sith shrine buried beneath the Jedi temple on Coruscant continuously leeched away their powers, implying that their power was at its greatest prior to the construction of the temple.
From the novel Tarkin:
The two of them were in Sidious’s lair, a small rock-walled enclosure beneath the deepest of the Palace’s several sublevels that had once been an ancient Sith shrine. That the Jedi had raised their Temple over the shrine had for a thousand years been one of the most closely guarded secrets of those Sith Lords who had perpetuated and implemented the revenge strategy of the Jedi Order’s founders. Even the most powerful of Dark Side Adepts believed that shrines of the sort existed only on Sith worlds remote from Coruscant, and even the most powerful of the Jedi believed that the power inherent in the shrine had been neutralized and successfully capped. In truth, that power had seeped upward and outward since its entombment, infiltrating the hallways and rooms above, and weakening the Jedi Order much as the Sith Masters themselves had secretly infiltrated the corridors of political power and toppled the Republic.
Thanks to @Null for leading me to a quote from a primary source.
The Jedi order existed for several thousand years before episode 1, while it would be difficult to narrow a time frame where the order was the strongest (by your definition) it was most certainly before the events of episodes 1-3
It would stand to reason that the Jedi order was strongest before the Sith faction formed however I cannot find a precise date and ultimately I do not think there is anything in canon one way or the other