I am connecting my device using core bluetooth and able to get sucessfull connection but in the iPhone setting the device connected without (i) info icon ,also not getting pair pop.
On connection a Pair pop up should come so i will be able to see my device in the iphone Paired devices list.
Is there a another way to connect so that my device is able to connect and visible in my iPhone setting.
You are likely confusing BLE connections with BR/EDR ("Classic") connections. When there is an (i), that indicates a BR/EDR connection. These are the kinds of connections that will appear in your "paired devices" list. These are commonly audio (headphones) or HID (keyboard/mouse) devices.
BLE connections do not display the (i) indicator. They will appear in the list when an app is actively connected to the device, but there is no persistent list of paired BLE devices. BLE devices generally do not involve a pairing step. Their encryption is most commonly handled by a mode called "Just Works" that does not require any user involvement.
If your app reads a secure BLE characteristic, then there will be a pairing event if required. You'd need to give all the details of how your device's characteristics are configured in order to discuss that further since there are quite a few options.
It is possible, and somewhat common in audio devices, to have both a BR/EDR and BLE connection. Core Bluetooth only interacts with the BLE connection (with some seldom-used exceptions). The two connections are completely separate. Even determining that the phone is connected to the same device over BR/EDR and BLE is quite challenging (I spent years developing solutions to that). For most applications, this is not a particular issue, so you'll need to provide more information if this is your problem.