Is there a way to create/modify connections through Airflow API

Connection is actually a model which you can use to query and insert a new connection

from airflow import settings
from airflow.models import Connection
conn = Connection(
        conn_id=conn_id,
        conn_type=conn_type,
        host=host,
        login=login,
        password=password,
        port=port
) #create a connection object
session = settings.Session() # get the session
session.add(conn)
session.commit() # it will insert the connection object programmatically.