After your paper is complete, consider submitting it for publication. Publishing your work is a great way to demonstrate to potential employers your writing ability and knowledge about a particular area of law. Here are some suggestions for places that may publish student work. Keep in mind that you may need to revise your paper for length or tone depending on the audience, but the work you've already done for your class or journal note is a great start.
Academic Legal Writing: Law Review Articles, Student Notes, Seminar Papers and Getting on Law Review by 
Scholarly writing for law students : seminar papers, law review notes, and law review competition papers by Professor Mark Wojcik offers advice in his October 2008 article, Get Published, that appeared in the ABA's Student Lawyer magazine.
Students can publish articles as notes or comments in academic law journals. Publishing in law journals outside of UIC Law journals can be done, although it is much more difficult since the publications are highly selective and you will be competing with professors, attorneys, and students from the journal’s school who may be given preference. The two most popular periods for journal submissions are mid-August through September and mid-March through April. If you are serious about trying to publish in an academic journal, read the chapter on Publishing & Publicizing in Academic Legal Writing: Law Review Articles, Student Notes, Seminar Papers and Getting on Law Review by Eugene Volokh available in the Academic Success Collection on the 6th floor of the library at KF250 .V65 2016.
Guidelines and requirements for submitting articles can vary from journal to journal. Some prefer direct submission by email, some require use of the Scholastica online submission system. Allen Rostron and Nancy Levit from UMKC School of Law have prepared a comprehensive chart outlining submission and formatting guidelines for journals associated with U.S. law schools: Information for Submitting Articles to Law Reviews & Journals. Bridget Crawford from Pace University School of Law has prepared a similar chart for submissions to the online supplements and companions of many of the top journals: Information for Submitting to Online Law Review Companions.
There is a growing preference by journals for authors to submit their articles using Scholastica. Scholastica is an online submission service used by hundreds of law journals. It is free to create an account, but there is a fee for each submission set by the individual journals. The service allows you to select and submit your article to multiple journals, though the fees can add up. More information can be found at Scholastica's Law Review Submissions Center and in its Author Guide.
All bar associations, including the American Bar Association, Chicago Bar Association, and the Illinois State Bar Association, have journals, magazines, and newsletters that are open to publishing pieces by students. Special Interest Sections, Divisions, and Committees of bar associations have numerous specialty publications that are read by hundreds of attorneys. Browse through old issues to find a publication or column that you think would be a good fit for your work, then email the editor. Editors are always looking for new pieces and authors to feature in their publications.
Bar association publications tend to be more practice-oriented since they are read by attorneys who are looking for news on how changes in the law will affect their day-to-day work. If your writing was prepared for a course or is more academic in nature, you may consider revising it to be tailored toward practitioners instead of a scholarly audience.
Writing contests are another great way to get published, plus there is an added bonus-many contests offer cash prizes. The ABA Young Lawyers Division maintains a list of writing contests on its site, and the AccessLex Institute also maintains a list of writing competitions.
Consider looking at blogs on your topic. Legal blogs will often discuss and link to or cite recent articles and can give you ideas for other publications that you might contact about publication opportunities. Writing for a blog is less prestigious than having an article published in a recognized journal or magazine, but it could lead to name recognition and networking opportunities with other attorneys in the field.
To find a blog about your area of law, check these legal blog directories: