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I just made a while loop which checks for message.published_timestamp(). Is there any convenient way to made this check in consumer?

Did you try to pass the following parameter to the subscribe function? initial_position=SubscriptionInitialPosition.Latest

I subscribe with initial_position=SubscriptionInitialPosition.Latest, but I perform operations on the incoming data and draw a graph. Meanwhile, new data still comes, and when I want to consume it, I actually receive a previously sent message, not the last one.

How many consumer instances do you have on the same subscription? Do you use a single or multiple subscriptions? And which type of subscription?

Multiple users can consume this topic from front end. So, there are multiple subscriptions. Consumer type is exclusive.

Could you share some code?

do you use a unique subscription name for each exclusive consumer? Can you share the output of the following command?

pulsar-admin topic stats <topic name>