It is possible for wild birds to mate with domestic chickens, although it is relatively rare. The resulting offspring would likely be a hybrid between the chicken and the wild bird species, which would vary depending on the species of the wild bird.
However, it's important to note that wild birds carrying diseases or parasites can transmit these infections to your chickens, which can be a serious health risk for your flock. Wild birds can also compete with your chickens for food and resources, which can lead to stress and overcrowding in the coop.
To prevent wild birds from accessing your coop and nesting areas, it's important to secure your coop with appropriate netting, fencing, or other protective measures. Additionally, be sure to monitor your flock for signs of illness or parasitic infection and take appropriate measures to prevent the spread of disease.