Step-1: Log into your account https://ap-south-1.console.aws.amazon.com/rds
Step-2: Click on databases >> Detail of the database >> Click on the networking 
Step-3: Click on the first box under Instance >> DB instance parameter group >> Click on the default one 
Step-4: Search 'max_connections' and click on the radio button and then edit it
Step-5: Replace the value box by: {DBInstanceClassMemory/125828}
Step-6: If it doesn't accept then create a new parameter group and add this value
Step-6: Now you need to back to the database detail panel and click on the 'Modify' option
Step-7: Scroll-down and see the option 'Database options' under 'Additional configuration'
Step-8: Select 'DB parameter group' and update it	
 

More: https://repost.aws/knowledge-center/rds-mysql-max-connections