Thyristors are turned on by applying gate pulse current sufficiently long enough to latch the thyristor into "ON" state. After this removal of gate current has no effect on the conduction state of the thyristor. However some highly interdigitted thyristors do required low level of gate current (called back-porch current) to keep them into good conduction state. Hence increse in gate current after the thyristor is latched on do not decrease the conduction losses. On the other hand increasing the gate peak current during turn-on phase decreases the turn-on losses. I hope this helps.

Your description is the impression of a lot of people, because the thyristors are used mostly in AC, such that the thyristor will switch to cut-off when the AC voltage hit zero periodically. As a result, to maintain a thyristor in turn on state, the gate has to be keep high and a gate current has to be supply. Depending on how high is the gate current, the thyristor will be turn on with different turn on time. The longer the turn on time, the higher the conduction loss at the transition state. Since this is being done periodically in AC source, the accumulated conduction loss at each AC cycle will be high enough that needs to be taken care of.

During turn on i think switching loss increases with the turn on time,how the conduction loss could be higher? Please provide some clarification

The resistance of the thyristor at the transition state between cut off and turn on is large, and cause conduction loss. This transition time (from cut off to turn on) will depends on the gate current. As a result, the conduction loss will depends on the gate current.