Be consistent with your Facebook contentand express diversity. The larger your fanbase the more FB Likes, Comments and Shares you will receive. By using Targeted ad campaigns or other social media strategies you can attain fans more rapidly.
Know your niche and choose quotes that resonate with your audience.
Visual imagery will capture the attention usually resulting in shares and comments. So post an image along with your quote.
Choose a good time of the day to post your quote to Facebook.
A Facebook user has around 250 friends on an average. When someone likes your page it automatically lets all their friends know that they have endorsed you, your product or your service. The moment someone likes your page they get subscribed to receive your updates. This means you can continue to interact with them and build the relationship.
You can get likes by joining a relevant group. Ensure that the groups you join have similar interests to those promoted by your page. You should try and promote your page to that particular group. You will get many people liking your page as a result of this.