Wounded Pigeon in my balcony
If you have a cat carrier then trying to intice it inside with some food would be a good idea. Try to contact your local wildlife vet for information on whether they would be willing to treat the animal. If you think it may be injured then I wouldn't reccomened handling the bird as you may hurt it further, but if you do need to then handle it by placing both hands over the wings in order to pick it up (https://www.rspb.org.uk/birds-and-wildlife/advice/how-you-can-help-birds/injured-and-baby-birds/if-you-find-an-injured-bird/) . In addition the bird could have gotten used to its injury and learned to live with it so you could monitor it for a bit and see how it's getting on. Hope it turns out alright.
If you live in the UK here is some advice from the RSPB: https://www.rspb.org.uk/birds-and-wildlife/advice/how-you-can-help-birds/injured-and-baby-birds/sick-and-injured-birds-faqs/#:~:text=For%20most%20injured%20birds%2C%20place,how%20you%20can%20help%20it.