Yes, both Jira and osTicket offer a Free Trial.
Jira is designed for Large Enterprises, Medium Business and Small Business.
osTicket is designed for Individuals, Large Enterprises, Medium Business and Small Business.
Pricing for Jira Starts at $6.25/User/Month when Billed Yearly whereas for osTicket Starts at $9/User/Month.
Some top alternatives to Jira includes Trello, Confluence, Asana, SwiftKanban, Kanbanize, ClickUp, Height, Kanban Tool, Kanban Zone and KanbanFlow.
Some top alternatives to osTicket includes Zendesk Support, Zoho Desk, Tidio Helpdesk, Freshservice, Jira Service Desk, Freshdesk, HelpDesk, SysAid, UVdesk, Jitbit Helpdesk, eStreamDesk, ReadyDesk, Spiceworks Help Desk, HESK, BoldDesk and GLPI.