How the packet is routed between two host from same sub-net and associated with same AP?

Question

Given host 'A' and 'B' have IP 10.10.0.5 and 10.10.0.8 respectively, the sub-net mask for both are 255.255.255.0, both 'A' and 'B' are associated and connected to the same AP, and the AP is connected to a switch at the interface 'X'.

'A' sends some packet to 'B'. If while 'A' is transmitting the packets and 'B' is in the transmission range of 'A', 'B' should hear his MAC address but CSMA-CA along with IEEE802.11(infrastructure mode) impose that 'B' needs to receive packets from only AP. Which route the packet should take?

+---+    
| A +--1-->+----+      +----+
+---+      |    +--2-->+    |
           | AP |      | SW |
+---+      |    +<--3--+    |
| B +<--4--+----+      +----+
+---+    

or

+---+    
| A +--1-->+----+
+---+      |    |
           | AP |
+---+      |    |
| B +<--2--+----+
+---+ 

Answer 1

Packets are routed, at layer-3, by a router. The Wi-Fi frames, at layer-2, are bridged by the WAP from one host to another host. In infrastructure mode, all frames are sent through the WAP.

A router, or any other network device, including a switch, will play no part unless the two hosts are on different networks. The second scenario you posited is what happens in infrastructure mode if both hosts are on the same LAN and WAP.

Answer 2

CSMA-CA along with IEEE802.11(infrastructure mode) impose that 'B' needs to receive packets from only AP

CSMA-CA doesn't impose this limitation. Even if direct communication between the clients was taking place (for example "adhoc" mode), CSMA-CA would still be in use.

It is the use of infrastructure mode that imposes the limitation that clients send all traffic to the AP (assuming no use of features such as 802.11z/TDLS).

Which route the packet should take?

In a basic 802.11 network, generally speaking traffic from A to B will leave A to the AP and the AP would then transmit the data back to B.

The exception is if there is some mechanism to prevent client-to-client traffic configured on the AP (i.e. client isolation). Depending on the hardware and specific configuration in use, the traffic may be dropped by the AP or it may forward the traffic to the L3 gateway to be processed (and possibly returned to B).