How to check whether any long running session is going on a particular schema?

You can use below query to get session specific details and add any kind of filter you want.

SELECT es.session_id
    ,es.program_name
    ,es.login_name
    ,es.nt_user_name
    ,es.login_time
    ,es.host_name
    ,es.cpu_time
    ,es.total_scheduled_time
    ,es.total_elapsed_time
    ,es.memory_usage
    ,es.logical_reads
    ,es.reads
    ,es.writes
    ,st.text
FROM sys.dm_exec_sessions es
    LEFT JOIN sys.dm_exec_connections ec 
        ON es.session_id = ec.session_id
    LEFT JOIN sys.dm_exec_requests er
        ON es.session_id = er.session_id
    OUTER APPLY sys.dm_exec_sql_text (er.sql_handle) st
WHERE es.session_id > 50    -- < 50 system sessions
ORDER BY es.cpu_time DESC

Further to that you can also use below query to identify the long running SQL in a session that could performance specific problems.

SELECT 
    substring(text,qs.statement_start_offset/2
        ,(CASE    
            WHEN qs.statement_end_offset = -1 THEN len(convert(nvarchar(max), text)) * 2 
            ELSE qs.statement_end_offset 
        END - qs.statement_start_offset)/2) 
    ,qs.plan_generation_num as recompiles
    ,qs.execution_count as execution_count
    ,qs.total_elapsed_time - qs.total_worker_time as total_wait_time
    ,qs.total_worker_time as cpu_time
    ,qs.total_logical_reads as reads
    ,qs.total_logical_writes as writes
FROM sys.dm_exec_query_stats qs
    CROSS APPLY sys.dm_exec_sql_text(qs.sql_handle) st
    LEFT JOIN sys.dm_exec_requests r 
        ON qs.sql_handle = r.sql_handle
ORDER BY 3 DESC